Question

Using two special right triangles, solve for x when the side lengths are 25, 16, and 22.

a. x ≈ 12
b. x ≈ 14
c. x ≈ 18
d. x ≈ 20

Answer 1

In this case, the value of x for the given triangle is approximately 12 (option a).

Step-by-step explanation:

To solve for x in the given triangle, we can use the Pythagorean theorem. The theorem states that in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse.

We have two special right triangles with side lengths:

Triangle 1: a = 16, b = 22, c = 25

Triangle 2: a = 22, b = 16, c = 25

Using the Pythagorean theorem, we can solve for x:

Triangle 1: x² + 16² = 25² => x² + 256 = 625 => x² = 369 => x ≈ √369 ≈ 19.21

Triangle 2: x² + 22² = 25² => x² + 484 = 625 => x² = 141 => x ≈ √141 ≈ 11.87

Therefore, the value of x for the given triangle is approximately 12 (option a).