Question

The hypotenuse of a right triangle is 5 inches. The lengths of the two legs are given by two consecutive integers. Find the lengths of the two legs.

Please walk me through it, I want to find the answer, I just need help getting there. :)

Answer 1

Its a 3,4,5 triangle. This is a common triangle you should get familiar with and memorize. To figure it out though: If you know the hypotenuse is 5, then according to the Pythagorean Theorem, the sum of the squares of the legs must be 5 (a^2 +b^2 = c^2, or leg1^2 + leg2^2 = 5^2), so you must find two numbers whose squares add to 25. Since they must be integers, a trial and error approach would work. The first few integers squared are 1, 4, 9, 16, 25. 16 and 9 add to 25 so they work. Their square roots are 4 and 3, so those are the leg lengths.

Answer 2

ooooh, ok, I understand. Thank you, next question