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Chapter 8: Q26. (page 492)

MULTIPLE CHOICE A rectangle has a length that is 2 inches longer than its width. The area of the rectangle is 48 square inches. What is the length of the rectangle?

F 48 in.

G 8 in.

H 6 in.

J 2 in.

Short Answer

Expert verified

The length of the rectangle is 8 in.

Step by step solution

01

Step 1. Convert.

Convert given information in the equation form.

Let Iand wbe the length and width of the rectangle respectively, such that,

l=2+w

02

Step 2. Write the formula of the area of a rectangle.

The area of the rectangle is given by A=l脳w.

Replace Aby 48 and Iby 2+winto A=l脳w.

2+w脳w=48w2+2w=48

03

Step 3. Subtract.

Subtract from both sides of the given equation.

w2+2w鈭�48=48鈭�48=0

04

Step 4. Factor by using GCF.

Factor by using GCF to get the form xy=0.

w+8w鈭�6=0

05

Step 5. Apply zero product property.

Apply zero product property to the given equation, w+8w鈭�6=0.

w+8=0orw鈭�6=0w=鈭�8w=6

As the value of length cannot be negative, therefore, the value of role="math" localid="1647952357609" w, that is, the width of the rectangle is 6 in.

Therefore, the length of a rectangle is 8 in and as option G completely matches with the obtained answer, option G is the correct answer.

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