Question

A triangle has side lengths of x, 2x, and 45. If the length of the longest side is 45, what value of x makes the triangle a right triangle?

a) x = 9
b) x = 12
c) x = 15
d) x = 18

Answer 1

Using the Pythagorean theorem, we can find the value of x that makes the triangle a right triangle. None of the given options is the correct answer.

Step-by-step explanation:

In a right triangle, the Pythagorean theorem can be used to determine the relationship between the lengths of the three sides. The theorem states that the sum of the squares of the lengths of the two shorter sides (legs) is equal to the square of the length of the longest side (hypotenuse). So in this case, we have x² + (2x)² = 45², where x is the length of the shorter leg and 2x is the length of the longer leg.

Simplifying the equation, we get x² + 4x² = 2025. Combining like terms, we have 5x² = 2025. Dividing both sides by 5, we find that x² = 405. Taking the square root of both sides, we get x = ± √405. Since x cannot be negative in this case, we take the positive square root, so x = √405.

Calculating √405, we find that x is approximately equal to 20.12. Therefore, none of the given options (a, b, c, d) is the correct value of x. The correct answer is not listed.