Question

for the following right triangle, find the side length x.

Explanation:

Step1: Apply Pythagorean theorem

For a right triangle, the Pythagorean theorem states that \( a^2 + b^2 = c^2 \), where \( a \) and \( b \) are the legs, and \( c \) is the hypotenuse. Here, \( a = 9 \), \( b = 40 \), and \( c = x \). So we have \( 9^2 + 40^2 = x^2 \).

Step2: Calculate the squares

\( 9^2 = 81 \) and \( 40^2 = 1600 \). Then \( 81 + 1600 = x^2 \).

Step3: Sum the values

\( 81 + 1600 = 1681 \), so \( x^2 = 1681 \).

Step4: Take the square root

Take the square root of both sides: \( x = \sqrt{1681} = 41 \).

Answer:

41