# Thread: hypotenuse question

1. ## hypotenuse question

the length of one leg of a right triangle is 7cm more than that of the other leg. The length of the hypotenuse is 3cm more than double that of the shorter leg. Find the lengths of each of the three sides.

Thanks

2. Originally Posted by euclid2
the length of one leg of a right triangle is 7cm more than that of the other leg. The length of the hypotenuse is 3cm more than double that of the shorter leg. Find the lengths of each of the three sides.

Thanks
Right angled triangle means Pythagoras' theorem applies.
So
Let's have A as the hypotenuse, B as the long leg and C as the short leg, as you put it.
A = 2C + 3 from The length of the hypotenuse is 3cm more than double that of the shorter leg.
and
B = C + 7 from the length of one leg of a right triangle is 7cm more than that of the other leg.
Since Pythagoras' theorem applies we know that A^2 = B^2 + C^2.
ie. (2C + 3)^2 = (C+7)^2 + C^2
4C^2 + 12C + 9 = C^2 + 14C + 49 + C^2
2C^2 - 2C -40 = 0
C^2 - C -20 = 0.
(C - 5)(C + 4) = 0.
So C = 5 or -4.
And since you can't have a negative length, C = 5.
And if C = 5, B=C+7=12, A = 2C+3 = 13.

3. thank you very much i really appreciate it