How to find the length of the side of a rhombus - Intermediate Geometry

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Question

Given that a rhombus has a perimeter of , find the length of one side of the rhombus.

Answer

The perimeter of a rhombus is equal to , where the length of one side of the rhombus.

Since , we can set up the following equation and solve for .

$124=4\times (S)$

$S=\frac{124}{4}=31$

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Question

A rhombus has an area of square units and a height of . Find the length of one side of the rhombus.

Answer

To find the length of a side of the rhombus, work backwards using the formula:

$A=(base\times height)$

Since we are given the area and the height we plug these values in and solve for the base.

$360=(base\times 8)$

$base=\frac{360}{8}=45$

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Question

A rhombus has an area of square units, and a height of . Find the length of one side of the rhombus.

Answer

To find the length of a side of the rhombus, work backwards using the area formula:

$Area=(base\times height)$

Since we are given the area and the height we plug these values in and solve for the base.

$69=(base\times 6)$

$base=\frac{69}{6}=11.5$

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Question

A rhombus has a perimeter of . Find the length of one side of the rhombus.

Answer

To solve for the length of one side of the rhombus, apply the perimeter formula:

,

the length of one side of the rhombus.

Since we are given the area we plug this value in and solve for .

$S=\frac{720}{4}=180$

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Question

A rhombus has an area of square units, and an altitude of . Find the length of one side of the rhombus.

Answer

Since the area is equal to square units, use the formula:

$A=(base\times altitude)$

Since we are given the area and the height, we plug these values in and solve for the base.

$39=(base\times 3)$

$base=\frac{39}{3}=13$

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Question

The perimeter of a rhombus is equal to . Find the length of one side of the rhombus.

Answer

Since

The solution is:

, where the length of one side of the rhombus.

Thus,

$S=\frac{520}{4}=130$

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Question

If a rhombus has a base that is $\frac{4}{3}$ times greater than the height and the height of the rhombus is equal to , find the length of one side of the rhombus.

Answer

To find the length of a side of the rhombus, multiply times $\frac{4}{3}$ .

Thus, the solution is:

$\frac{9}{1}\times\frac{4}{3}=\frac{36}{3}=12$

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Question

A rhombus has an area of square units, and an altitude of . What is the length of one side of the rhombus?

Answer

To find the length of a side of the rhombus, work backwards using the area formula:

$Area=(base\times height)$

Since we are given the area and the height, we plug these values into the equation and solve for the base.

$645=(base\times 15)$

$base=\frac{645}{15}=43$

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Question

Given that a rhombus has an area of square units and a height of , find the length of one side of the rhombus.

Answer

To find the length of a side of the rhombus, work backwards using the area formula:

$Area=(base\times height)$

Since we are given the area and the height, we plug these values into the equation and solve for the base.

$85=(base\times height)$

$85=(base\times 5)$

$base=\frac{85}{5}=17$

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Question

If a rhombus has a perimeter of , what is the length of one side of the rhombus?

Answer

To find the length of a side of the rhombus, apply the formula: , where is equal to the length of a side of the rhombus.

Since we are given the perimeter we plug that value into the equation and solve for .

Therefore the solution is:

$S=\frac{14}{4}=3.5$

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Question

Given that a rhombus has a perimeter of , find the length of a side of the rhombus.

Answer

To find the length of one side of the rhombus, apply the formula:

, where is the side length.

Since we are given the perimeter, we plug that value into the equation and solve for .

$S=\frac{90}{4}=22.5$

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Question

Given that a rhombus has an area of square units, and a height of . What is the length of one side of the rhombus?

Answer

To find the length of a side of the rhombus, work backwards using the area formula:

$Area=(base\times height)$

Since we are given the area and the height, we plug these values into the equation and solve for the base.

$70=(base\times height)$

$70=(base\times 5)$

$base=\frac{70}{5}=14$

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Question

Find the length of a side of a rhombus if it has diagonals possessing the following lengths: and .

Answer

Recall that the diagonals of a rhombus bisect each other and are perpendicular to one another.

In order to find the length of the side, we can use Pythagorean's theorem. The lengths of half of the diagonals are the legs, and the length of the side of the rhombus is the hypotenuse.

First, find the lengths of half of the diagonals.

$\frac{\text{Diagonal 1}}{2}=\frac{2}{2}=1$

$\frac{\text{Diagonal 2}}{2}=\frac{4}{2}=2$

Next, substitute these half diagonals as the legs in a right triangle using the Pythagorean theorem.

$1^2+2^2=\text{side length}^2$

$\text{side length}^2=1+4=5$

$\text{side length}=\sqrt5$

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Question

Find the length of a side of a rhombus if it has diagonals possessing the following lengths: and .

Answer

Recall that the diagonals of a rhombus bisect each other and are perpendicular to one another.

In order to find the length of the side, we can use Pythagorean's theorem. The lengths of half of the diagonals are the legs, and the length of the side of the rhombus is the hypotenuse.

First, find the lengths of half of the diagonals.

$\frac{\text{Diagonal 1}}{2}=\frac{4}{2}=2$

$\frac{\text{Diagonal 2}}{2}=\frac{10}{2}=5$

Next, substitute these half diagonals as the legs in a right triangle using the Pythagorean theorem.

$2^2+5^2=\text{side length}^2$

$\text{side length}^2=4+25=29$

$\text{side length}=\sqrt{29}$

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Question

Find the length of a side of a rhombus if it has diagonals possessing the following lengths: and .

Answer

Recall that the diagonals of a rhombus bisect each other and are perpendicular to one another.

In order to find the length of the side, we can use Pythagorean's theorem. The lengths of half of the diagonals are the legs, and the length of the side of the rhombus is the hypotenuse.

First, find the lengths of half of the diagonals.

$\frac{\text{Diagonal 1}}{2}=\frac{12}{2}=6$

$\frac{\text{Diagonal 2}}{2}=\frac{20}{2}=10$

Next, substitute these half diagonals as the legs in a right triangle using the Pythagorean theorem.

$6^2+10^2=\text{side length}^2$

$\text{side length}^2=36+100=136$

$\text{side length}=2\sqrt{34}$

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Question

Find the length of a side of a rhombus if it has diagonals possessing the following lengths: and .

Answer

Recall that the diagonals of a rhombus bisect each other and are perpendicular to one another.

In order to find the length of the side, we can use Pythagorean's theorem. The lengths of half of the diagonals are the legs, and the length of the side of the rhombus is the hypotenuse.

First, find the lengths of half of the diagonals.

$\frac{\text{Diagonal 1}}{2}=\frac{14}{2}=7$

$\frac{\text{Diagonal 2}}{2}=\frac{22}{2}=11$

Next, substitute these half diagonals as the legs in a right triangle using the Pythagorean theorem.

$7^2+11^2=\text{side length}^2$

$\text{side length}^2=49+121=170$

$\text{side length}=\sqrt{170}$

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Question

Find the length of a side of a rhombus if it has diagonals possessing the following lengths: and .

Answer

Recall that the diagonals of a rhombus bisect each other and are perpendicular to one another.

In order to find the length of the side, we can use Pythagorean's theorem. The lengths of half of the diagonals are the legs, and the length of the side of the rhombus is the hypotenuse.

First, find the lengths of half of the diagonals.

$\frac{\text{Diagonal 1}}{2}=\frac{16}{2}=8$

$\frac{\text{Diagonal 2}}{2}=\frac{18}{2}=9$

Next, substitute these half diagonals as the legs in a right triangle using the Pythagorean theorem.

$8^2+9^2=\text{side length}^2$

$\text{side length}^2=64+81=145$

$\text{side length}=\sqrt{145}$

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Question

Find the length of a side of a rhombus if it has diagonals possessing the following lengths: and .

Answer

Recall that the diagonals of a rhombus bisect each other and are perpendicular to one another.

In order to find the length of the side, we can use Pythagorean's theorem. The lengths of half of the diagonals are the legs, and the length of the side of the rhombus is the hypotenuse.

First, find the lengths of half of the diagonals.

$\frac{\text{Diagonal 1}}{2}=\frac{6}{2}=3$

$\frac{\text{Diagonal 2}}{2}=\frac{8}{2}=4$

Next, substitute these half diagonals as the legs in a right triangle using the Pythagorean theorem.

$3^2+4^2=\text{side length}^2$

$\text{side length}^2=9+16=25$

$\text{side length}=5$

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Question

Find the length of a side of a rhombus if it has diagonals possessing the following lengths: and .

Answer

Recall that the diagonals of a rhombus bisect each other and are perpendicular to one another.

In order to find the length of the side, we can use Pythagorean's theorem. The lengths of half of the diagonals are the legs, and the length of the side of the rhombus is the hypotenuse.

First, find the lengths of half of the diagonals.

$\frac{\text{Diagonal 1}}{2}=\frac{10}{2}=5$

$\frac{\text{Diagonal 2}}{2}=\frac{24}{2}=12$

Next, substitute these half diagonals as the legs in a right triangle using the Pythagorean theorem.

$5^2+12^2=\text{side length}^2$

$\text{side length}^2=25+144=169$

$\text{side length}=13$

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Question

Find the length of a side of a rhombus if it has diagonals possessing the following lengths: and .

Answer

Recall that the diagonals of a rhombus bisect each other and are perpendicular to one another.

In order to find the length of the side, we can use Pythagorean's theorem. The lengths of half of the diagonals are the legs, and the length of the side of the rhombus is the hypotenuse.

First, find the lengths of half of the diagonals.

$\frac{\text{Diagonal 1}}{12}=\frac{2}{2}=6$

$\frac{\text{Diagonal 2}}{2}=\frac{16}{2}=8$

Next, substitute these half diagonals as the legs in a right triangle using the Pythagorean theorem.

$6^2+8^2=\text{side length}^2$

$\text{side length}^2=36+64=100$

$\text{side length}=10$

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