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Start by calling the shortest side 
. We then know that the longer leg (call it 
) is 7 feet longer i.e. 
. We also know that the hypotenuse, 
is 1 foot more than twice the short leg i.e. 
. We now have 3 unknowns but only 2 equations to solve them. Luckily we know this is a right triangle so we can use the Pythagorean Theorem as our third equation:
Substituting known values:
This is now an equation in one variable and can be solved algebraically for. Back-substitution can then be used for the other sides.
Substituting known values:
This is now an equation in one variable and can be solved algebraically for