A right triangle has one leg that is 7 feet longer than the other leg, and the hypotenuse is 8 feet longer than the shortest side. Find the lengths of the sides of the right triangle.

Question

whpalmer4 · Answer

the lengths of the sides of a right triangle $a,b$ and hypotenuse $c$ will satisfy the equation $$a^2+b^2=c^2$$

You know that $a = b+7$ ("one leg is 7 feet longer than the other leg") and $c = 8+b$ ("the hypotenuse is 8 feet longer than the shortest side")

If you substitute using those equations, you should be able to write an equation in terms of only one variable, then solve it.  Use the value you get to find the values of the other two.

whpalmer4 · Answer

You'll get two answers, but only one of them will make sense as the length of a side of a triangle.

anonymous · Answer

Can you tell me how to set up the equation?

whpalmer4 · Answer

I think I already did :-)

take $$a^2+b^2=c^2$$
Now replace $a$ with $(b+7)$
Then replace $c$ with $(8+b)$

Expand it all and solve (you'll get a quadratic equation in terms of $b$\)

That will give you the value of $b$, which is the shortest side.  Then find $a = b+7$ and $c = 8+b$ for the other two sides.