# The length of a swimming pool is 8m longer than its width and the area is 105m^2 . question.express the length and width form an equation and solve the misiing length and width

1
by senrefolo

2015-06-04T20:46:21+08:00

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I can't explain much but here is how to solve that.

The formula for the are of a rectangle is A = LW

Width = w
Length = 8m longer than the width = w + 8

Area of the swimming pool = Length x Width = 105
= w + 8 ( w)
= w² + 8w
= w² + 8w = 105
w² + 8w - 105 = 0
(Factor this out)
w² + 8w - 105 = 0
( w + 15 ) (w - 7) = 0
w + 15 = 0, w - 7 = 0
w  = -15,  w = 7

Since there is no -15m in length, then the length and width is:

Length of the swimming pool = 15m
Width of the swimming pool   = 7m

Overall, they are equal to:  15m x 7m = 105, CORRECT
15m - 7m = 8m, CORRECT