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Chapter 6: Q. 461 (page 638)

The area of a rectangular placemat is 168square inches. Its length is two inches longer than the width. Find the length and width of the placemat.

Short Answer

Expert verified

The length and width of the placemat is 14inches and 12inches.

Step by step solution

01

Step 1. Assume the integers.

Assume width of the placemat to be xinches and length of the placemat to be x+2inches.

Area of placemat=length脳width

Substitute the values in the above equation,

role="math" localid="1644852659113" 168=xx+2......(i)168=x2+2x

Bring all the terms to one side,

x2+2x-168=0

02

Step 2. Factor the equation.

On factoring,

x2+14x-12x-168=0xx+14-12x+14=0x+14x-12=0

Then,

x+14=0x=-14

As we know, width cannot be negative. Hence, it is not considered.

localid="1644853096959" x-12=0x=12inches

Then the length,

localid="1644853107588" x+12=12+2=14inches

03

Step 3. Check the answers.

Substitute the obtained values of the length and width in equation (i),

14脳12=168168=168

This is true.

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