Question 954409: Jeremy is going to help his neighbor build a patio similar in shape to his patio. Jeremy's neighbor's patio will have twice the area of Jeremy's patio. How can Jeremy use the dimensions of his patio to determine the dimensions of his neighbor’s patio?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! if he doubles the dimensions of his patio, then the neighbor's patio will have an area that's 4 times as large.
so he can't double the dimensions.
however, let's take a look at the formula and see what we can do.
A = L*W
2A = 2*L*W
since 2 = sqrt(2) * sqrt(2), then we can get:
2A = sqrt(2)*L*sqrt(2)*W.
So, if we multiply each of the dimensions of our patio by sqrt(2), then we should get an area for the neighbor's patio of 2 * the area of our patio.
As an example:
Suppose that our patio is 5 * 8 feet.
the area of our patio is therefore 40 square feet.
we multiply each of our dimensions by sqrt(2) and we get:
neighbor's patio will be 5 * sqrt(2) * 8 * sqrt(2) = 5 * 8 * 2 = 80 square feet.
the area of the neighbor's patio is now double the area of our patio.
5 * sqrt(2) is equal to 7.071067812 feet which is roughly 7 feet 1 inch.
8 * sqrt(2) is equal to 11.313708499 feet which is roughly 11 feet 4 inches.
the area of our neighbor's patio will be pretty close to double the area of our patio.
our patio will still be 40 square feet.
the neighbor's patio will be 7 feet 1 inch times 11 feet 4 inches which is equal to 80.2777.....
that's pretty close.
we could try to get closer but it's not practical.
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