SOLUTION: The top of a kitchen island is a piece of granite that has an area of 15ft^2. It is 3.5 ft longer than it is wide. Find the dimensions of the surface.

Question 1082006: The top of a kitchen island is a piece of granite that has an area of 15ft^2. It is 3.5 ft longer than it is wide. Find the dimensions of the surface.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
length * width = area.
let L = length and W = width and you get:
L * W = area
since area = 15, you get:
L * W = 15
since L = W + 3.5, you get:
(W + 3.5) * W = 15
simplify to get W^2 + 3.5W = 15
subtract 15 from both sides of the equation to get:
W^2 + 3.5W - 15 = 0
multiply both sides of this equation by 2 to get:
2W^2 + 7W - 30 = 0
factor this equation to get:
(2W - 5) * (W + 6) = 0
W can be either 5/2 or -6
since it can't be minus, then it has to be 5/2.
when W = 5/2, L = W + 3.5 becomes L = 5/2 + 7/2 = 12/2
L * W becomes 5/2 * 12/2 = 60/4 = 15
solution looks good.
if you can't factor the quadratic equation, then use the quadratic formula.
you will get the same answer.
the graph of W^2 + 3.5W - 15 = y and the graph of 2W^2 + 7W - 30 = y look like this.
as you can see, the roots of both equations are the same, even though the equations are different.
they have the same values only when y = 0.
$$$

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