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Chapter 7: Q58. (page 349)

Suppose the length and width of rectangle A are each 40% of the length and width of rectangle B. Is the area of rectangle A 40% of the area of rectangle B? Justify your answer.

Short Answer

Expert verified

Area of rectangle A is not 40% of the area of rectangle B.

Because by calculation, Area of rectangle A is 16% of area of rectangle B.

Step by step solution

01

Step 1. Given Information.

Length and width of rectangle A are each 40% of the length and width of rectangle B.

02

Step 2. Calculate the area of rectangle B.

Assume, length =xunits

And width =yunits

Therefore,

area=length鈰�width=x鈰�y=xyunitsquare

03

Step 3. Calculate the area of rectangle A.

Length = 40% of the length of rectangle B.

=40%ofx=40100x[writepercentasfraction]=25x[simplify]

Width = 40% of the width of rectangleB.

=40%ofy=40100y[writepercentasfraction]=25y[simplify]

Therefore,

area=length鈰�width=25x鈰�25y=425xyunitsquare[multiply]

04

Step 4. Conclusion.

Converting 425 into percent

425=0.16[convertfractionintodecimal]0.16=16%[convertdecimalintopercentbyshiftingthedecimaltwoplacesandwritingwithpercentsign]

Therefore,

Area of rectangle A is 16% of area of rectangle B.

Area of rectangle A is not 40% of the area of rectangle B.

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