Chapter 6: Q. 461 (page 638)

The area of a rectangular placemat is $168$ square 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 $14$ inches and $12$ inches.

Step by step solution

Step 1. Assume the integers.

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

Area of placemat $= l e n g t h \times w i d t h$

Substitute the values in the above equation,

role="math" localid="1644852659113" $168 = x (x + 2) . . . . . . (i) 168 = x^{2} + 2 x$

Bring all the terms to one side,

$x^{2} + 2 x - 168 = 0$

Step 2. Factor the equation.

On factoring,

$x^{2} + 14 x - 12 x - 168 = 0 x (x + 14) - 12 (x + 14) = 0 (x + 14) (x - 12) = 0$

Then,

$x + 14 = 0 x = - 14$

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

localid="1644853096959" $x - 12 = 0 x = 12 i n c h e s$

Then the length,

localid="1644853107588" $x + 12 = 12 + 2 = 14 i n c h e s$

Step 3. Check the answers.

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

$14 \times 12 = 168 168 = 168$

This is true.

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

Short Answer

Step by step solution

Step 1. Assume the integers.

Step 2. Factor the equation.

Step 3. Check the answers.

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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

Step by step solution

Step 1. Assume the integers.

Step 2. Factor the equation.

Step 3. Check the answers.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Probability and Statistics

Applied Mathematics

Logic and Functions

Statistics

Geometry

Study anywhere. Anytime. Across all devices.

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