Question

Use the polynomial identity to determine which values of x and y generate the values of the sides of the following right triangle.

73
48
55

a) x = 24, y = 7
b) x = 7, y = 24
c) x = 25, y = 48
d) x = 48, y = 25

Answer 1

The correct values for x and y that generate the sides of the given right triangle with lengths 73, 48, and 55 are x = 24 and y = 7, which corresponds to option (a).

Step-by-step explanation:

To determine the values of x and y that generate the sides of the right triangle with lengths 73, 48, and 55, we can use the Pythagorean theorem and the polynomial identity for Pythagorean triples. The Pythagorean theorem states that for a right triangle, the sum of the squares of the two shorter sides is equal to the square of the longest side.

In this case, the Pythagorean identity is x² + y² = z², where x and y are the shorter sides, and z is the longest side (the hypotenuse). Substituting the given values, we get 24² + 7² = 73².

Calculating further, 576 + 49 = 625. Hence, 625 = 625, which is true.

Now, let's check the other options:

b) 7² + 24² = 49 + 576 = 625, which is true.

c) 25² + 48² = 625 + 2304 = 2929, which is not true.

d) 48² + 25² = 2304 + 625 = 2929, which is not true.

Therefore, the correct values are x = 24 and y = 7 from option (a), satisfying the Pythagorean theorem and forming a right triangle with side lengths 73, 48, and 55.