Perimeter and Sides of Triangles - GED Math

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Question

Note: Figure NOT drawn to scale.

Refer to the above diagram. Evaluate .

Answer

The altitude perpendicular to the hypotenuse of a right triangle divides that triangle into two smaller triangles similar to each other and the large triangle. Therefore, the sides are in proportion. The hypotenuse of the triangle is equal to

$\sqrt{5^{2}+12^{2}} = \sqrt{25+144} = \sqrt{169} =13$ .

Therefore, we can set up a proportion and solve for :

$\frac{X}{12} = \frac{12}{13}$

$\frac{X}{12}\cdot 12 = \frac{12}{13} \cdot 12$

$X = \frac{144}{13} = 11\frac{1}{13}$

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Question

A triangle has sides of length 36 inches, 3 feet, and one yard. Choose the statement that most accurately describes this triangle.

Answer

One yard is equal to three feet, or thirty-six inches. The three given sidelengths are equal to one another, making this an equilateral triangle.

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Question

If $\Delta MNO \cong \Delta PQR$ , then which segment is congruent to $\overline{NO}$ ?

Answer

A congruency statement about two triangles implies nothing about the relationship between two sides of the same triangle, so we can eliminate $\overline{MO}$ . Also, the length of a segment with endpoints on two different triangles depends on their positioning, not their congruence, so we can eliminate $\overline{NQ}$ .

Since and are in the same positions in the name of the first triangle as and , $\overline{NO}$ and $\overline{QR}$ are corresponding sides of congruent triangles, and

$\overline{NO} \cong \overline{QR}$ .

Since the letters of the name of a segment are interchangeable, this statement can be rewritten as

$\overline{NO} \cong \overline{RQ}$ ,

making $\overline{RQ}$ the correct choice.

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Question

If the base of an equilateral triangle is 16cm, find the perimeter.

Answer

To find the perimeter of a triangle, we will use the following formula:

where a, b, and c are the lengths of the sides of the triangle.

Now, we know the base of the triangle is 16cm. Because it is an equilateral triangle, all sides are equal. Therefore, all sides are 16cm. So, we get

$P = 16\text{cm} +16\text{cm} +16\text{cm}$

$P = 48\text{cm}$

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Question

The perimeter of an equilateral triangle is 36in. Find the length of one side.

Answer

The formula to find the perimeter of an equilateral triangle is

where a is the length of one side of the triangle. Because it is an equilateral triangle, all sides are equal. Therefore, we can use any side in the formula. To find the length of one side, we will solve for a.

Now, we know the perimeter of the equilateral triangle is 36in. So, we will substitute and solve for a. We get

$36\text{in} = 3a$

$\frac{36\text{in}}{3} = \frac{3a}{3}$

$12\text{in} = a$

$a = 12\text{in}$

Therefore, the length of one side of the equilateral triangle is 12in.

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Question

Find the perimeter of an equilateral triangle with a side having a length of 17in.

Answer

To find the perimeter of a triangle, we will use the following formula:

where a, b, and c are the lengths of the sides of the triangle.

Now, we know one side of the triangle has a length of 17in. Because it is an equilateral triangle, all sides are equal. Therefore, all sides are 17in. So, we can substitute. We get

$P = 17\text{in} +17\text{in} +17\text{in}$

$P = 51\text{in}$

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Question

An equilateral triangle has a perimeter of 69in. Find the length of one side.

Answer

The formula to find the perimeter of an equilateral triangle is

where a is the length of one side of the triangle. Because an equilateral triangle has 3 equal sides, we can use any side in the formula. To find the length of one side, we will solve for a.

Now, we know the perimeter of the triangle is 69in. So, we can substitute and solve for a. We get

$69\text{in} = 3a$

$\frac{69\text{in}}{3} = \frac{3a}{3}$

$23\text{in} = a$

$a = 23\text{in}$

Therefore, the length of one side of the equilateral triangle is 23in.

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Question

The perimeter of an equilateral triangle is 42cm. Find the length of one side.

Answer

To find the perimeter of an equilateral triangle, we will use the following formula:

where a is the length of one side. An equilateral triangle has 3 equal sides, so we can use any side in the formula. To find the length of one side, we will solve for a. Now, we know the perimeter of the triangle is 42cm. So, we will substitute and solve for a. We get

$42\text{cm} = 3a$

$\frac{42\text{cm}}{3} = \frac{3a}{3}$

$14\text{cm} = a$

$a = 14\text{cm}$

Therefore, the length of one side of the equilateral triangle is 14cm.

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Question

A triangle has the sides of , , and . What is the perimeter of the triangle?

Answer

The three sides of the triangle are known. Add all the sides together.

The answer is:

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Question

Suppose the perimeter of a triangle is $\frac{1}{3}x-9$ . What must be the side length?

Answer

There are three sides in a triangle.

To determine the length of a side, multiply the quantity by one-third.

$\frac{1}{3}(\frac{1}{3}x-9) = \frac{1}{9}x -3$

The answer is: $\frac{1}{9}x -3$

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Question

The perimeter of an equilateral triangle is 45in. Find the length of one side.

Answer

The formula to find the perimeter of an equilateral triangle is

where a is the length of one side of the triangle. Because it is an equilateral triangle, all sides are equal. Therefore, we can use any side in the formula. To find the length of one side, we will solve for a.

Now, we know the perimeter of the triangle is 45in. So, we can substitute and solve for a. So, we get

$45\text{in} = 3a$

$\frac{45\text{in}}{3} = \frac{3a}{3}$

$15\text{in} = a$

$a = 15\text{in}$

Therefore, the length of one side of the equilateral triangle is 15in.

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Question

An equilateral triangle has a perimeter of 123in. Find the length of one side.

Answer

The formula to find the perimeter of an equilateral triangle is

where a is the length of one side of the triangle. An equilateral triangle has 3 equal sides, so we can use any side in the formula. To find the length of one side, we will solve for a.

Now, we know the perimeter of the triangle is 123in. So, we will substitute and solve for a. We get

$123\text{in} = 3a$

$\frac{123\text{in}}{3} = \frac{3a}{3}$

$41\text{in} = a$

$a = 41\text{in}$

Therefore, the length of one side of the equilateral triangle is 41in.

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Question

Use the following triangle to answer the question:

Find the perimeter.

Answer

To find the perimeter of a triangle, we will use the following formula:

where a, b, and c are the lengths of the sides of the triangle.

Now, given the triangle

we can see it has lengths of 9in, 3in, and 10in. Knowing this, we can substitute into the formula. We get

$P = 9\text{in} + 3\text{in} + 10\text{in}$

$P = 22\text{in}$

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Question

Use the following triangle to answer the question:

Find the perimeter.

Answer

To find the perimeter of a triangle, we will use the following formula:

where a, b, and c are the lengths of the sides of the triangle.

So, given the following triangle

we can see it has sides of length 8cm, 4cm, and 6cm. So, we can substitute. We get

$P = 8\text{cm} + 4\text{cm} + 6\text{cm}$

$P = 18\text{cm}$

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Question

Find the perimeter of a triangle if the side length is .

Answer

The triangle is not specified whether if it is an isosceles, right triangle, or equilateral triangle.

We only can conclude that there's only one known side. There is insufficient information to find the total perimeter of the triangle.

The answer is: $\textup{Not enough information.}$

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Question

If the side of an equilateral triangle is , what is the perimeter?

Answer

The perimeter of an equilateral triangle is three times the given side length, since all three sides are congruent.

Multiply the known side by three.

Simplify the inner terms.

The answer is:

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Question

Use the following triangle to answer the question:

Find the perimeter.

Answer

To find the perimeter of a triangle, we will use the following formula:

where a, b, and c are the lengths of the sides of the triangle.

Now, given the triangle

we can see it has sides with lengths of 10ft, 6ft, and 12ft. So, we can substitute. We get

$P = 10\text{ft} + 6\text{ft} + 12\text{ft}$

$P = 28\text{ft}$

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Question

Determine the perimeter if a known side of a triangle is .

Answer

The perimeter of an equilateral triangle would be known, but the type of triangle is unknown in the problem statement.

The perimeter of a triangle requires three known sides. Since only one side is given, we do not have enough information to determine the perimeter.

The answer is: $\textup{Not enough information.}$

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Question

Use the following triangle to answer the question:

Find the perimeter.

Answer

To find the perimeter of a triangle, we will use the following formula:

where a, b, and c are the lengths of the sides of the triangle.

Now, given the triangle

we can see it has sides with lengths 10ft, 6ft, and 12ft. So, we can substitute. We get

$P = 10\text{ft} + 6\text{ft} + 12\text{ft}$

$P = 28\text{ft}$

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Question

Use the following equilateral triangle to answer the question:

Find the perimeter.

Answer

To find the perimeter of a triangle, we will use the following formula:

where a, b, and c are the lengths of the sides of the triangle.

Now, given the triangle

we can see one side is 4ft. Because it is an equilateral triangle, all sides are equal. Therefore, all sides are 4ft. So, we can substitute. We get

$P = 4\text{ft} + 4\text{ft} + 4\text{ft}$

$P = 12\text{ft}$

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