High School

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The length of a rectangle is 8 feet more than its width. The area of the rectangle is 97 ft². Determine the length and width of the rectangle.

Answer :

Answer:

L = [tex]\sqrt{113}[/tex] +4

W = [tex]\sqrt{113}[/tex] -4

or L = 14.63 ft, and W = 6.63 ft

Step-by-step explanation:

Let L be the length and W the width.

We are told that the "length of a rectangle is 8 feet more than its width:"

L = W+8

Area of the rectangle is given by L*W, and is 97 [tex]ft^{2}[/tex]

L*W = 97

Substituting L=W+8, we get:

(W+8)W=97 [tex]ft^{2}[/tex]

[tex]W^{2}[/tex] + 8W = 97

[tex]W^{2}[/tex] + 8W - 97 = 0

The roots to this equation are:

  • -4-[tex]\sqrt{113}[/tex], and
  • [tex]\sqrt{113}[/tex] -4

Only the second gives a positive value, so W = [tex]\sqrt{113}[/tex] -4

Since L=W+8, the length, L, is [tex]\sqrt{113}[/tex] -4 + 8 or [tex]\sqrt{113}[/tex] +4

In decimal:

L = 14.63 ft, and W = 6.63 ft

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Rewritten by : Barada