How to find the perimeter of a figure - HSPT Math

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Question

A rectangular garden has an area of $80: \mbox{m^2}$ . Its length is meters longer than its width. How much fencing is needed to enclose the garden?

Answer

We define the variables as $w = \mbox{width}$ and $l = \mbox{length} = w + 2$ .

We substitute these values into the equation for the area of a rectangle and get $A_{\mbox{rectangle} }= wl = w(w + 2) = 80$ .

or

Lengths cannot be negative, so the only correct answer is . If , then .

Therefore, $\mbox{perimeter }= 2w + 2l = 16 + 20 = 36:\mbox{m}$ .

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Question

What is the circumference of a circle with a radius of 5?

Answer

The formula for circumference is $\dpi{100} \pi d$ or $\dpi{100} 2\pi r$ .

Since we are given the radius, we will use $\dpi{100} 2\pi r$ .

$\dpi{100} 2\pi r=2\pi (5)=10\pi$

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Question

What is the perimeter of a square with a side length of 4?

Answer

The formula for the perimeter of a square is $\dpi{100} 4s$ , where $\dpi{100} s$ is the length of one side of the square.

So $\dpi{100} 4\cdot (4)=16$

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Question

If the perimeter of a rectangle is 40, and the width of the rectangle is 8, what is the length of the rectangle?

Answer

The formula for the perimeter of a rectangle is $\dpi{100} P=2l+2w$ , where $\dpi{100} l$ is the length of the rectangle and $\dpi{100} w$ is the width.

Plug in the numbers that we are given into the equation.

$\dpi{100} 40=2l +2(8)$

$\dpi{100} 40=2l +16$

$\dpi{100} 40-16=2l +16-16$

$\dpi{100} 24=2l$

$\dpi{100} \frac{24}{2}=\frac{2l}{2}$

$\dpi{100} l=12$

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Question

What is the perimeter of a rectangle with a base of 4 and a height of 8?

Answer

When searching for the perimeter of a rectangle we are looking for the sum of the lengths of all of the sides enclosing the figure. In this case there are four sides, two that are the base and two that are the height. To find the perimeter we add all four of them together.

Therefore the equation for the perimeter of a rectangle is

In this case the equation looks like this

Multiply the numbers together

Then add them to get the answer

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Question

What is the height of a rectangle with a perimeter of 30 and base of 12?

Answer

The perimeter of a rectangle is the sum of four sides, two that are the base and two that are the height. To find the perimeter we add all four of them together.

Therefore the equation for the perimeter of a rectangle is

In this example we plug in the base and the perimeter so the equation looks like this

Perform the multiplication to get

Subtract from both sides to arrive at

Then divide by 2 to find the height $\frac{2(Height)}{2}=\frac{6}{2}$

The answer

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Question

What is the perimeter of a square with a side legnth of 8?

Answer

When searching for the perimeter of a square we are looking for the sum of the lengths of all of the sides enclosing the figure. In this case there are four sides that are all equal length. To find the perimeter we add all four of them together or multiply the side length by four.

In this example the equation looks like this:

Multiply the numbers together to get .

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Question

What is the radius of a circle with a circumference of $64\pi$ ?

Answer

To find the radius of a circle given the circumference we must first know the equation for the circumference of a circle which is

$Circumference=2\pi(r)$

Then we plug in the circumference into the equation for yielding $64\pi=2\pi(r)$

We then divide each side by $2\pi$ : $\frac{64\pi}{2\pi}=32$

We then have the answer for which is .

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Question

What is the perimeter of a square with a diagonal of $\sqrt2$ ?

Answer

To find the perimeter of the square, find the length of the side. Write the formula to find the length of the side.

$d=\sqrt{s^2+s^2}$

Substitute the diagonal and solve for the side.

$\sqrt2=\sqrt{s^2+s^2}$

First, square each side to get rid of the square root.

Divide 2 by each side to isolate the

Take the square root of each side.

Since there are four sides in a square, multiply the side length by four to get the perimeter.

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Question

An equilateral triangle has a length of . What is the perimeter?

Answer

The perimeter of an equilateral triangle is three times the length of its side.

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Question

What is the perimeter of a square with a side length of ?

Answer

Write the perimeter formula for a square.

Substitute the side length in the formula and simplify.

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Question

A circle has radius 8. The circumference of the circle is 40% of what number?

Answer

The circumference of a circle is its radius mulitplied by $2 \pi$ . The radius is 8, so the circumference is

$8 \cdot 2 \pi = 16 \pi$ .

To find the number of which this is 40%, divide this by 40%, or $\frac{40 }{100}$ :

$16 \pi \div\frac{40 }{100} = 16 \pi \div\frac{2}{5} = 16 \pi \cdot \frac{5} {2} = \frac{80 \pi} {2} = 40 \pi$

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Question

A ladder 30 feet long leans against a house. The top of the ladder is feet above the ground. In terms of , how far along the ground is the bottom of the ladder from the house?

Answer

The ladder, which is 30 feet long, is the hypotenuse of a right triangle whose legs are the line from the top of the ladder to the ground, which has length feet, and the line from the bottom of the ladder horizontally to the house, whose length we will call feet. See the diagram below.

By the Pythagorean Theorem,

$M^{2}+N^{2} = 30 ^{2} = 900$

Solving for :

$M^{2}+N^{2} - N^{2} = 900 - N^{2}$

$M^{2}= 900 - N^{2}$

$M = \sqrt{900 - N^{2}}$ , the correct choice.

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Question

$\bigtriangleup ABC \sim \bigtriangleup DEF$ .

$\angle B$ is a right angle.

$m \angle C = 45 ^{\circ }$ .

Is $\bigtriangleup DEF$ scalene, isosceles, or equilateral - or can it be determined?

Answer

Corresponding angles of similar triangles are congruent, so

$m \angle E = m \angle B = 90 ^{\circ }$

$m \angle F = m \angle C = 45 ^{\circ }$

The degree measures of the angles of a triangle total 180, so

$m \angle D =180^{\circ } - (m \angle F +m \angle E )$

$m \angle D =180^{\circ } - (90^{\circ } +45^{\circ } ) = 45^{\circ }$

Since $\angle D$ and $\angle F$ are congruent, by the Isosceles Triangle Theorem,

$\overline{EF} \cong \overline{DE}$

making $\bigtriangleup DEF$ isosceles.

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Question

What is the perimeter of the polygon below?

Answer

To find the area of a perimeter, we add all of the side lengths together.

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Question

What is the perimeter of the polygon below?

Answer

To find the area of a perimeter, we add all of the side lengths together.

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Question

What is the perimeter of the polygon below?

Answer

To find the area of a perimeter, we add all of the side lengths together.

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Question

What is the perimeter of the polygon below?

Answer

To find the area of a perimeter, we add all of the side lengths together.

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Question

What is the perimeter of the polygon below?

Answer

To find the area of a perimeter, we add all of the side lengths together.

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Question

What is the perimeter of the polygon below?

Answer

To find the area of a perimeter, we add all of the side lengths together.

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