SSAT Middle Level Quantitative - How to find the perimeter of a rectangle

Rectangle

Give the perimeter of the rectangle in the above diagram.

$26 \frac{1}{5} \textrm{ in}$

$13 \frac{1}{10} \textrm{ in}$

$52 \frac{2}{5} \textrm{ in}$

$42 \textrm{ in}$

$84 \textrm{ in}$

Explanation

The perimeter of a rectangle can be calculated by multiplying two by the sum of the length and width of the rectangle.

$2\left ( 7 \frac{1}{2} +5 \frac{3}{5} \right )$

$=2 \left (\frac{7 \cdot 2 + 1}{2} + \frac{5\cdot 5 + 3}{5} \right )$

$= 2 \left (\frac{15}{2} + \frac{28}{5} \right )$

$= 2 \left (\frac{15 \times 5}{2 \times 5} + \frac{2 \times28}{2 \times5} \right )$

$= 2 \left (\frac{75}{10} + \frac{56}{10} \right ) = \frac{2}{1} \cdot \frac{131}{10} = \frac{131}{5} = 26 \frac{1}{5}$

The perimeter of the rectangle is $26 \frac{1}{5}$ inches.

Rectangle

Give the perimeter of the rectangle in the above diagram.

$38 \textrm{ cm}$

$19 \textrm{ cm}$

$80.64 \textrm{ cm}$

$40.32 \textrm{ cm}$

$76 \textrm{ cm}$

Explanation

The perimeter of a rectangle is the sum of the length and the width, multiplied by 2:

$2 (12.6 + 6.4) = 2 \cdot 19 = 38$

The rectangle has a perimeter of 38 centimeters.

Find the perimeter of the rectangle shown below

Screen shot 2015 11 10 at 9.55.29 pm

Explanation

The perimeter of a rectangle, or any shape, is the distance around the outside. You add up the length of each side to find this number. The coordinates of the points are . You need to find the distance between each point. The short side is units, and the longer side is units.

$(8\times2)+(10\times2)=16+20=36$

Rectangles

Note: Figure NOT drawn to scale.

Refer to the above diagram. Give the ratio of the perimeter of the large rectangle to that of the smaller rectangle.

The correct answer is not given among the other choices.

Explanation

Opposite sides of a rectangle are congruent.

The large rectangle has perimeter

The smaller rectangle has perimeter

The ratio is

$\frac{240}{100} = \frac{240 \div 20 }{100\div 20 } = \frac{12}{5}$ ; that is, 12 to 5.

A rectangle has an area of . The length of each side is a whole number. What is NOT a possible value for the rectangle's perimeter?

Explanation

Since each side is a whole number, first find the whole number factors of . They are and , and , and , and and . These sidelengths correspond to perimeters of , , , and , respectively. Thus, is answer.

Rectangle

Give the perimeter of the above rectangle in centimeters, using the conversion factor centimeters per yard.

$2,011.68 \textrm{ cm}$

$1,005.84 \textrm{ cm}$

$2,194.56 \textrm{ cm}$

$1,097.28 \textrm{ cm}$

$4,389.12 \textrm{ cm}$

Explanation

The perimeter of the rectangle is yards. To convert this to centimeters, multiply by the given conversion factor:

$91.44 \times 22 = 2,011.68$ centimeters.

Rectangles

Note: Figure NOT drawn to scale.

Refer to the above diagram. Give the perimeter of the red polygon.

The perimeter cannot be determined from the information given.

Explanation

Since opposite sides of a rectangle have the same measure, the missing sidelengths can be calculated as in the diagram below:

Rectangles

The sidelengths of the red polygon can now be added to find the perimeter:

Rectangle ABCD has an area of . If the width of the rectangle is , what is the perimeter?

Explanation

The area of a rectangle is found by multiplying the length times the width. The question tells you the width is and the area is .

Thus the length is 8. $\left ( 40 \div5\right)$ .

To find the perimeter you add up all of the sides.

The width of a rectangle is one-third of its length. If the width is given as what is the perimeter of the rectangle in terms of ?

$2w+\frac{1}{3}w$

Explanation

The perimeter of a rectangle is the sum of its sides.

The sum of the widths is and since the width is one-third of the length, each length is . Since there are lengths we get a total of . Widths + lengths =