Question

for the following right triangle, find the side length x. right triangle image with legs 6 and 8, hypotenuse 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, \( a = 6 \), \( b = 8 \), and \( c = x \). So we have \( 6^2 + 8^2 = x^2 \).

Step2: Calculate the squares

\( 6^2 = 36 \) and \( 8^2 = 64 \). Then \( 36 + 64 = x^2 \).

Step3: Sum the values

\( 36 + 64 = 100 \), so \( x^2 = 100 \).

Step4: Take the square root

Taking the square root of both sides, \( x = \sqrt{100} = 10 \).

Answer:

10