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ISEE Middle Level Math : Plane Geometry

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Example Questions

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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Example Question #31 : Quadrilaterals

The perimeter of a rectangle with a length of 10x and a width of is $64\ in$ . Find .

Possible Answers:

Correct answer:

Explanation:

We know that:

Perimeter=2(a+b)

where:

$a=Length \ of\ the\ rectangle$

$b= Width\ of\ the\ rectangle$

So we can write:

$64=2(10x+6x)\Rightarrow 10x+6x=32\Rightarrow 16x=32\Rightarrow x=2$

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Example Question #5 : How To Find The Perimeter Of The Rectangle

Rectangles

Note: Figure NOT drawn to scale.

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

Possible Answers:

120

140

240

340

The perimeter cannot be determined from the information given.

Correct answer:

240

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:

40 + 80 + 20 + 30 + 20 + 50 = 240

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Example Question #125 : Quadrilaterals

The width of a rectangle is , the length is , and the perimeter is 72. What is the value of ?

Possible Answers:

Correct answer:

Explanation:

Start with the equation for the perimeter of a rectangle:

P=l+l+w+w=2l+2w

We know the perimeter is 72, the length is , and the width is . Plug these values into our equation.

72=2(6x)+2(3x)

Multiply and combine like terms.

72=12x+6x

72=18x

Divide by 18 to isolate the variable.

$\frac{72}{18}=x$

Simplify the fraction by removing the common factor.

$\frac{72}{18}=\frac{72\div18}{18\div18}=\frac{4}{1}=4$

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Example Question #126 : Quadrilaterals

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.

Possible Answers:

2:1

12:5

The correct answer is not given among the other choices.

16:7

8:3

Correct answer:

12:5

Explanation:

Opposite sides of a rectangle are congruent.

The large rectangle has perimeter

40 + 80 + 40 + 80 = 240 .

The smaller rectangle has perimeter

20 + 30 + 20 + 30 = 100 .

The ratio is

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

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Example Question #11 : How To Find The Perimeter Of A Rectangle

What is the perimeter of a rectangle with a width of 3 and a length of 10?

Possible Answers:

Correct answer:

Explanation:

The formula for the perimeter of a rectangle is $\dpi{100} Perimeter=2l+2w$ .

Plug in our given values to solve:

$\dpi{100} Perimeter = 2(20)+2(3)$

$\dpi{100} Perimeter = 20+6$

$\dpi{100} Perimeter = 26$

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Example Question #13 : How To Find The Perimeter Of A Rectangle

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

Possible Answers:

Correct answer:

Explanation:

The perimeter of a rectangle is represented by the following formula, in which W represents width and L represents length:

2W+2L= Perimeter

Given that the width is inches and that the perimeter is inches, the following applies:

$2\cdot 2+2L=14$

4+2L=14

Next, subtract from each side.

2L=10

Now, divide each side by .

This gives us

L=5

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Example Question #131 : Quadrilaterals

Rectangle

Give the perimeter of the above rectangle in centimeters, using the conversion factor 91.44 centimeters per yard.

Possible Answers:

$1,097.28 \textrm{ cm}$

$2,194.56 \textrm{ cm}$

$2,011.68 \textrm{ cm}$

$4,389.12 \textrm{ cm}$

$1,005.84 \textrm{ cm}$

Correct answer:

$2,011.68 \textrm{ cm}$

Explanation:

The perimeter of the rectangle is 8 + 3 + 8 + 3 = 22 yards. To convert this to centimeters, multiply by the given conversion factor:

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

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Example Question #221 : Plane Geometry

Find the perimeter of a rectangle whose length is 6 and width is 5.

Possible Answers:

Correct answer:

Explanation:

To solve, simply use the formula for the perimeter of a rectangle.

In this particular case the length and width are,

l=6, w=5

Thus,

P=2(l+w)=2*(6+5)=2*11=22

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Example Question #12 : How To Find The Perimeter Of The Rectangle

A rectangle has a length of 9 centimeters and a width of 5 centimeters. Find the perimeter.

Possible Answers:

23cm

14cm

28cm

19cm

Correct answer:

28cm

Explanation:

The formula for the perimeter of a rectangle is:

P = 2L + 2W

where

L = length

P = 2 (9+5)

$P = 2 \times 14$

P = 28cm

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All ISEE Middle Level Math Resources

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ISEE Middle Level Math : Plane Geometry

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

All ISEE Middle Level Math Resources

Example Questions

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

Example Question #31 : Quadrilaterals

Example Question #5 : How To Find The Perimeter Of The Rectangle

Example Question #125 : Quadrilaterals

Example Question #126 : Quadrilaterals

Example Question #11 : How To Find The Perimeter Of A Rectangle

Example Question #13 : How To Find The Perimeter Of A Rectangle

Example Question #131 : Quadrilaterals

Example Question #221 : Plane Geometry

Example Question #12 : How To Find The Perimeter Of The Rectangle

All ISEE Middle Level Math Resources

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