Question

A rectangular shelf has an area of 288 square inches. Its perimeter is 72 inches. What are the dimensions of the shelf?

Answer 1

Answer:

• 24 inches x 12 inches

Step-by-step explanation:

Perimeter

• 2l + 2w = 72
• l + w = 36

Area

• lw = 288

From the perimeter

• Reaarrange the equation of the perimeter so that it equates to one of the variables
• l = 36 - w

Substituting in the area formula

• (36 - w)(w) = 288
• 36w - w² = 288
• w² - 36w + 288 = 0
• w² - 24w - 12w + 288 = 0
• w(w - 24) - 12(w - 24) = 0
• (w - 12)(w - 24) = 0
• w = 24, 12

The greater value of the two will be the length, and lesser value will be the width.

Dimensions are : 24 inches x 12 inches

Answer 2

Answer:

perimeter=4×length

so 72= 4l

divide through by 4

length=18