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Chapter 11: Q. 235 (page 1148)

In the following exercises, solve the problem using a system of equations.

The perimeter of a rectangle is 52 cm and its area is 165 cm2. Find the length and width of the rectangle.

Short Answer

Expert verified

15,11,11,15

Step by step solution

01

Step 1. Given information.

The value of the perimeter of the rectangle is 52 cm and the area is 165 cm2

02

Step 2. Forming the equations.

Let lbe the length and wbe the width of the rectangle in cm. Then the perimeter and the area of the rectangle will be 2l+wand l脳w, respectively. According to the given conditions,

2l+w=52--->(1)l脳w=165--->(2)

03

Step 3. Solving the equations.

Solving equation (2) for l gives

l=165w

Substituting this in equation (1) and then solve it:

2165w+w=52165w+w=26165+w2=26wMultiplyingbothsidesbyww2-26w+165=0w2-15w-11w+165=0Factorizingtheequationw-15w-11=0

So, wither w-15=0or w-11=0

When w-15=0, then w=15and from equation (2), l=16515=11

When w-11=0, then w=11and from equation (2), l=16511=15

Hence, as ordered pairs, the solution can be expressed as

15,11,11,15

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