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ISEE Upper Level Math : How to find the perimeter of a rectangle

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Example Questions

Example Question #1 : How To Find The Perimeter Of A Rectangle

A >0 . Which is the greater quantity?

(a) The perimeter of the square on the coordinate plane with vertices (0,0), (A,0 ), (0,A), (A,A)

(b) The perimeter of the rectangle on the coordinate plane with vertices (0,0), (A+2,0 ), (0,A-2), (A+2,A-2)

Possible Answers:

It is impossible to tell from the information given.

(b) is greater.

(a) and (b) are equal.

(a) is greater.

Correct answer:

(a) and (b) are equal.

Explanation:

(a) The square has sidelength A - 0 = A , and therefore has perimeter .

(b) The rectangle has width A + 2 - 0 = A +2 and height A - 2 - 0 = A - 2 , so therefore has perimeter

$\left ( A + 2 \right ) + \left ( A - 2 \right ) + \left ( A + 2 \right ) + \left ( A - 2\right ) = A + A + A + A + 2- 2 + 2 - 2 = 4A$ .

The perimeters are the same.

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Example Question #1 : How To Find The Perimeter Of A Rectangle

Your geometry book has a rectangular front cover which is 12 inches by 8 inches.

What is the perimeter of your book cover?

Possible Answers:

40 in^2

80 in^2

40 in

42 in

Correct answer:

40 in

Explanation:

Your geometry book has a rectangular front cover which is 12 inches by 8 inches.

What is the perimeter of your book cover?

Perimeter is the distance around the outside of a shape.

Perimeter of a rectangle can be found via the following:

$P_{rectangle}=2l+2w$

Plug in our length and width to find our answer:

P=2(12in)+2(8in)=24in+16in=40in

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Example Question #82 : Quadrilaterals

Your aunt and uncle live on a rectangular plot of land out in the countryside. The width of their plot is $\frac{3}{4}$ of a kilometer long. The length is twice the width. What is the total length of the perimeter of the plot of land?

Possible Answers:

6 km

4.5 km

2.25 km

3.6 km

Correct answer:

4.5 km

Explanation:

Begin by finding both the width and length.

We are told that the width is $\frac{3}{4}$ of a kilometer

Further, we are told that the length is twice the width. Write this as an equation and solve:

$l=2w=2\frac{3}{4}=\frac{6}{4}=1\frac{1}{2}$

Now, find the perimeter via the following:

$P=2l+2w\rightarrow 2(\frac{3}{4}km)+ 2(\frac{3}{2}km)=1\frac{1}{2}km+3km=4.5km$

So, our perimeter is 4.5 km

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ISEE Upper Level Math : How to find the perimeter of a rectangle

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

All ISEE Upper Level Math Resources

Example Questions

Example Question #1 : How To Find The Perimeter Of A Rectangle

Example Question #1 : How To Find The Perimeter Of A Rectangle

Example Question #82 : Quadrilaterals

All ISEE Upper Level Math Resources

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