Question 954409
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.