Question

The length of one leg of a right triangle is 9ft. The length of the hypotenuse is 3 feet longer than the other leg. Find the length of the hypotenuse and the other leg.

Answer 1

a^2 + b^2 = c^2

Since the hypotenuse (c) is 3 feet longer then the other leg (b) we can write the equation like this

9^2 +b^2 = (b+3)^2
81+b^2=b^2+6b+9

If you subtract b^2 from both sides they cancel each other out. You can also subtract 9 from both sides which will give you

72 = 6b

You divide both sides by 6 to give you b = 12

now you can solve for c in the original equation

9^2 +12^2 = c^2

81 + 144 = c^2

255 = c^2

take the square root of both sides

c = 15

So the other leg is 12 feet long and the hypotenuse is 15 feet long.

Answer 2

15, and 12.