Question

Find the length of the shorter leg of a right triangle if the longer leg is 7 feet more than the shorter leg and the hypotenuse is 7 feet less than twice the shorter leg.

Answer 1

You can use the pythagorean theorem.
$a^{2} + b^{2} = c^{2}$
Now lets write out what we know.

Shorter leg = x
Longer Leg = x + 7
Hypotenuse = x - 7

$a^{2} + b^{2} = c^{2}$
Now solve for x
$x^{2} + (x+7)^{2} = (2x-7)^{2}$
x = 28
Since you know x = 28, which is the shorter leg, you can solve for the rest by just plugging in 28 where x is located. For instance, longer let is x + 7 so 
28 + 7 = 35