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Chapter 6: Q. 325 (page 628)

The area of a rectangular carpet is 28square feet. The length is three feet more than the width. Find the length and the width of the carpet.

Short Answer

Expert verified

The length and the width of the rectangular carpet is4feet,7feet.

Step by step solution

01

Step 1. Assumption of integers.

Assume xfeetto be the width and x+3feetto be the length of the carpet.

Area of rectangular carpet=length脳width

Substitute the values in the equation of area,

28=xx+3x2+3x=28x2+3x-28=0......(i)

02

Step 2. Factor the equation.

On factoring,

x2+7x-4x-28=0xx+7-4x+7=0x+7x-4=0

Use the zero product property,

x+7=0x=-7

Then,

x-4=0x=4

As we know, the width of the carpet cannot be negative, so x=4.

Then the length of the carpet,

=x+3=4+3=7

03

Step 3. Check the answers.

Substitute the width and the length in equation (i),

4脳7=2828=28

This is true.

Hence, the width and the length of the rectangular carpet is4feet,7feet.

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