GED Math - Perimeter and Sides of Quadrilaterals

A rectangle has a diagonal of and a side length of . What is the perimeter of the rectangle?

Explanation

Notice that the question gives us the hypotenuse of a right triangle that has two sides of the rectangle as legs.

Use the Pythagorean Theorem to find the missing side of the rectangle.

$12^2=10^2+\text{side}^2$

$\text{side}^2=44$

$\text{side}=6.633$

Now, add together the sides to find the perimeter of the rectangle.

$\text{Perimeter}=10+10+6.633+6.633=33.266$

Make sure to round to two places after the decimal.

$\text{Perimeter}=33.27$

Find the perimeter of a rectangle with a length of 12in and a width that is a third of the length.

$32\text{in}$

$48\text{in}$

$36\text{in}$

$30\text{in}$

$24\text{in}$

Explanation

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

where l is the length and w is the width of the rectangle.

Now, we know the length of the rectangle is 12in. We know the width of the rectangle is a third of the length. Therefore, the width is 4in. So, we can substitute. We get

$P = 2(12\text{in}) + 2(4\text{in})$

$P = 24\text{in} + 8\text{in}$

$P = 32\text{in}$

Use the following rectangle to answer the question:

Rectangle4

Find the perimeter.

$32\text{cm}$

$63\text{cm}$

$16\text{cm}$

$30\text{cm}$

$28\text{cm}$

Explanation

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

where l is the length and w is the width of the rectangle.

Now, given the rectangle

Rectangle4

we can see the length is 9cm and the width is 7cm. So, we can substitute. We get

$P = 2(9\text{cm}) + 2(7\text{cm})$

$P = 18\text{cm} + 14\text{cm}$

$P = 32\text{cm}$

Find the perimeter of a square with a width of 12in.

$48\text{in}$

$144\text{in}$

$24\text{in}$

$36\text{in}$

$\text{There is not enough information to solve the problem.}$

Explanation

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

where a is any side of the square. Because a square has 4 equal sides, we can use any side within the formula.

Now, we know the square has a width of 12in. So, we can substitute. We get

$P = 4(12\text{in})$

$P = 48\text{in}$

If the side of a square has a length of , what must the perimeter be?

Explanation

The perimeter of a square is four times the length since, all four sides are congruent.

The answer is:

A square and a right triangle share a side as shown by the figure below.

Find the area of the square.

Explanation

Notice that the side of the square is the same as the hypotenuse of the right triangle.

Use Pythagorean's theorem to find the length of the hypotenuse.

$\text{Hypotenuse}=\sqrt{5^2+12^2}=\sqrt{169}=13$

Now that we have the length of a side of the square, find the area.

$\text{Area of Square}=13^2=169$

The ratio of the length of a rectangle to its width is 6 to 5. The perimeter of the rectangle is 99. Give its length.

$22\frac{1}{2}$

Explanation

The ratio of the length of a rectangle to its width is 6 to 5, so if we let be the length and be the width, the proportion statement for these dimensions is

$\frac{W} {L}= \frac{5}{6}$

Multiply both sides by ; this can be restated as

$\frac{W} {L}(L)= \frac{5}{6} (L)$

$W= \frac{5}{6} L$

The perimeter of the rectangle is equal to

Set this equal to 99 and set $W= \frac{5}{6} L$ :

$2L+2 \cdot \frac{5}{6} L = 99$

Simplify:

$\frac{12}{6}L+ \frac{10}{6} L = 99$

Collect like terms by adding coefficients:

$\left (\frac{12}{6}+ \frac{10}{6} \right )L = 99$

$\frac{22}{6} L = 99$

Reduce:

$\frac{11}{3}L = 99$

Multiply both sides by $\frac{3}{11}$ to solve for

$\frac{3}{11} \cdot \frac{11}{3}L =\frac{3}{11} \cdot 99$

$L =\frac{3}{11} \cdot \frac{99}{1}$

$L =\frac{3}{1} \cdot \frac{9}{1}$

the correct length.

The perimeter of a square is 72in. Find the length of one side.

$18\text{in}$

$36\text{in}$

$9\text{in}$

$54\text{in}$

$16\text{in}$

Explanation

To answer this, we will look at the formula for perimeter of a square. We get

where a is the length of one side of the square. Because a square has 4 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 square is 72\text{in}. So, we will substitute and solve for a. We get

$72\text{in} = 4a$

$\frac{72\text{in}}{4} = \frac{4a}{4}$

$18\text{in} = a$

$a = 18\text{in}$

Therefore, the length of one side of the square is 18in.

Rhombus

Note: Figure NOT drawn to scale.

Quadrilateral is a rhombus. Calculate its perimeter if:

Explanation

The four sides of a rhombus are congruent. Also, the diagonals of a rhombus are perpendicular bisectors to each other, so the four triangles they form are right triangles. Therefore, the Pythagorean theorem can be used to determine the common sidelength of Quadrilateral .