Question

The length of the shortest side of a right triangle is 8. The lengths of the other two sides are represented by two consecutive odd integers such that a leg is the first integer and the hypotenuse is the second integer. What are the two integers?

Answer 1

The two integers are;

x is 15 and

x + 2 is 17

Explanation:

The given parameters are;

The length of the shortest side = 8

The length of the other two sides are x and (x + 2) where x is an odd integer and hypotenuse side = x + 2

Therefore, we have;

(x + 2)² = 8² + x²

x² + 4·x + 4 = 8² + x²

x² - x² + 4·x = 8² - 4 = 64 - 4 = 60

4·x = 60

x = 15

Therefore, the hypotenuse side = x + 2 = 15 + 2 = 17

The two integers are thus;

x = 15 and

x + 2 = 17.

Answer 2

Answer: the 2 integers are 15 and 17

Explanation:

Let x represent the hypotenuse of the right angle triangle. Since the hypotenuse and the other leg are odd consecutive integers, then the other leg is x - 2 because x is longer

When a right angle triangle is formed, it means that

Hypotenuse² = opposite side² + adjacent side²

If the shortest side is 8, it means that

x² = (x - 2)² + 8²

x² = x² - 2x - 2x + 4 + 64

x² - x² + 2x + 2x = 68

4x = 68

x = 68/4 = 17

Therefore, the length of the other leg is

x - 2 = 17 - 2 = 15