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ddd [48]
2 years ago
15

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

Mathematics
2 answers:
scZoUnD [109]2 years ago
8 0

Answer:

  • 24 inches x 12 inches

Step-by-step explanation:

<u>Perimeter</u>

  • 2l + 2w = 72
  • l + w = 36

<u>Area</u>

  • lw = 288

<u>From the perimeter</u>

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

<u>Substituting in the area formula</u>

  • (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.

<u>Dimensions are</u> : 24 inches x 12 inches

<u />

scZoUnD [109]2 years ago
4 0

Answer:

perimeter=4×length

so 72= 4l

divide through by 4

length=18

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