Question

If the longer leg of a right triangle is 117, find a pair of missing sides that forms a primitive (non-reducible) Pythagorean triple with the longer leg. Your values must be under 160.

Enter the two values separated by a comma.

Answer 1

To find a pair of missing sides that forms a primitive Pythagorean triple with the longer leg of a right triangle, we can try different values of m and n. Let's try m = 12 and n = 5 to find the missing sides.

Step-by-step explanation:

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the two legs (a and b). In this case, we are given that the longer leg is 117. To find a primitive Pythagorean triple with the longer leg as one of the legs, we need to find positive integers m and n, where m > n, such that a = m^2 - n^2, b = 2mn, and c = m^2 + n^2. Since the values must be under 160, we can start by trying different values of m and n.

Let's try m = 12 and n = 5:

a = (12^2 - 5^2) = 119

b = 2(12)(5) = 120

c = (12^2 + 5^2) = 169

So a pair of missing sides that forms a primitive Pythagorean triple with the longer leg of 117 is 119, 120.