What's the step of solving this question
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What's the step of solving this question

[From: ] [author: ] [Date: 12-12-08] [Hit: ]
P.S. Full equation please!This gives you the possibility of the length being either 15m or -12m. Now obviously there is no such thing as a negative measurement so the length can only be 15m.The pool is 15m long and 12m wide.......
The width of a swimming pool is 3m less than its length. If its area is 180m^2, find the length and width of the pool.

P.S. Full equation please!

-
Width = x - 3
Length = x
Area of a rectangle = Length * Width
-----------------
Multiply the dimensions into each other and form an equation:

x(x - 3) = 180

Expand the brackets:

x^2 - 3x = 180

Move everything to one side:

x^2 - 3x - 180 = 0

Factor it out:

(x + 12) (x - 15) = 0

This gives you the possibility of the length being either 15m or -12m. Now obviously there is no such thing as a negative measurement so the length can only be 15m.

x = 15
x - 3 = 12

The pool is 15m long and 12m wide.

-
Area is the product of width and length. Let x be the length.
We know the width, is 3m less than the length, so (x-3) = width.
Area = Width x Length
180 = x (x -3) (Substituting values)
180 = x² - 3x
x² - 3x - 180 = 0 (putting into a quadratic)
(x - 15) (x + 12) = 0 (Factorising)
so x = 15, or x = -12.

Lengths cannot be negative, so only answer possible is x = 15.

So length = 15,
and width is 15 - 3, so width = 12.
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