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SSAT Middle Level Math : Rectangles

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Example Questions

Example Question #1 : Rectangles

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

Possible Answers:

6w+2

2w+4

Correct answer:

Explanation:

The sum of the widths is and since the width is half the length, each length is . Since there are 2 lengths we get a total perimeter of .

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Example Question #2 : Rectangles

L_lawn

The above figure shows the size and shape of a yard that is to be surrounded by some fence. How many feet of fence will be needed?

Note: all sides meet at right angles.

Possible Answers:

$665 \textrm{ ft}$

$935 \textrm{ ft}$

$750 \textrm{ ft}$

$650 \textrm{ ft}$

$565 \textrm{ ft}$

Correct answer:

$750 \textrm{ ft}$

Explanation:

The best way to see that 750 feet of fence are needed is to look at this augmented diagram.

Note that two of the sides are extended to form a smaller rectangle whose sides can be deduced by subtraction. Since opposite sides of a rectangle are congruent, this allows us to fill in the two missing sidelengths of the original figure.

L_lawn_2

Now add: $150+110+70+115+80+225 = 750 \textrm{ft}$

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Example Question #3 : Rectangles

Rectangle

Give the perimeter of the rectangle in the above diagram.

Possible Answers:

$40.32 \textrm{ cm}$

$80.64 \textrm{ cm}$

$38 \textrm{ cm}$

$19 \textrm{ cm}$

$76 \textrm{ cm}$

Correct answer:

$38 \textrm{ cm}$

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.

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Example Question #3 : How To Find The Perimeter Of A Rectangle

Rectangle

Give the perimeter of the rectangle in the above diagram.

Possible Answers:

$42 \textrm{ in}$

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

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

$84 \textrm{ in}$

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

Correct answer:

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

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.

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Example Question #4 : How To Find The Perimeter Of A Rectangle

Rectangle_1

Figure NOT drawn to scale.

Give the perimeter of the green polygon in the above figure.

Possible Answers:

380

The perimeter cannot be determined from the information given.

190

230

260

Correct answer:

230

Explanation:

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

Rectangle_2

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

P= 35 +60 + 35 + 15 + 20 + 30 + 20 + 15 = 230

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Example Question #4 : How To Find The Perimeter Of A Rectangle

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 ?

Possible Answers:

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

Correct answer:

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 = 2w + 6w = 8w

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Example Question #212 : Plane Geometry

You are given equilateral triangle $\Delta ABC$ and Rectangle ACDE

with AB = 25, CD = 40 .

What is the perimeter of Rectangle ACDE ?

Possible Answers:

160

115

130

180

Correct answer:

130

Explanation:

$\Delta ABC$ is equilateral, so AC = AB = 25 .

Also, since opposite sides of a rectangle are congruent,

DE = AC = 25 and AE = CD = 40

The perimeter of Rectangle ACDE is

AC + CD +DE + AE = 25 + 40 + 25 + 40 = 130

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Example Question #211 : Plane Geometry

A hectare is a unit of area equal to 10,000 square meters.

A 150-hectare plot of land is rectangular and is 1.2 kilometers in width. Give the perimeter of this land.

Possible Answers:

$5.4 \textrm{ km}$

$4.9 \textrm{ km}$

$2.45 \textrm{ km}$

$2.7 \textrm{ km}$

Correct answer:

$4.9 \textrm{ km}$

Explanation:

150 hectares is equal to $150 \times 10,000 = 1,500,000$ square meters.

The width of this land is 1.2 kilometers, or $1.2 \times 1,000 =1,200$ meters. Divide the area by the width to get:

$1,500,000 \div 1,200 = 1,250$ meters

The perimeter of the land is

$2 \left ( 1,200 + 1,250\right ) = 4,900$ meters, or $4,900 \div 1,000 = 4.9$ kilometers.

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Example Question #4 : Rectangles

The length of a rectangle is two times as long as the width. The width is equal to inches. What is the perimeter of the rectangle?

Possible Answers:

$\small 32\ in$

$\small 40\ in$

$\small 24\ in$

$\small 16\ in$

Correct answer:

$\small 24\ in$

Explanation:

l=2w=2(4)=8

P=l+w+l+w=2l+2w=2(8)+2(4)=16+8=24

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Example Question #6 : How To Find The Perimeter Of A Rectangle

How many meters of fence are needed to enclose a rectangular field that has a length of 1000 meters and a width of 100 meters?

Possible Answers:

$100,000\ meters$

$10,000\ meters$

$2200\ meters$

$2000\ meters$

$1100\ meters$

Correct answer:

$2200\ meters$

Explanation:

The perimeter of a rectangle is simply the sum of the four sides:

$1000+1000+100+100=2200\; meters$

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SSAT Middle Level Math : Rectangles

Study concepts, example questions & explanations for SSAT Middle Level Math

All SSAT Middle Level Math Resources

Example Questions

Example Question #1 : Rectangles

Example Question #2 : Rectangles

Example Question #3 : Rectangles

Example Question #3 : How To Find The Perimeter Of A Rectangle

Example Question #4 : How To Find The Perimeter Of A Rectangle

Example Question #4 : How To Find The Perimeter Of A Rectangle

Example Question #212 : Plane Geometry

Example Question #211 : Plane Geometry

Example Question #4 : Rectangles

Example Question #6 : How To Find The Perimeter Of A Rectangle

All SSAT Middle Level Math Resources

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