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!
P.S. Full equation please!
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Width = x - 3
Length = x
Area of a rectangle = Length * Width
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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.
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.
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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.
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.