80.6k views
13 votes
A rectangular shelf has an area of 288 square inches. Its perimeter is 72 inches. What are the dimensions of the shelf?

I need help with this

2 Answers

5 votes

Answer:

  • 24 inches x 12 inches

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

User Amrit
by
7.9k points
12 votes

Answer:

perimeter=4×length

so 72= 4l

divide through by 4

length=18

User Ugo
by
8.4k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories