Question

The length of a rectangle is 8 feet more than its width. the area of the rectangle is 97 ft.² determine the length and width of the rectangle

Answer 1

L =
`√(113)` +4

W =
`√(113)` -4

or L = 14.63 ft, and W = 6.63 ft

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
`ft^(2)`

L*W = 97

Substituting L=W+8, we get:

(W+8)W=97
`ft^(2)`

`W^(2)` + 8W = 97


`W^(2)` + 8W - 97 = 0

The roots to this equation are:

• -4-
  `√(113)`, and
• 
  `√(113)` -4

Only the second gives a positive value, so W =
`√(113)` -4

Since L=W+8, the length, L, is
`√(113)` -4 + 8 or
`√(113)` +4

In decimal:

L = 14.63 ft, and W = 6.63 ft