Question

A right triangle has legs of lengths 8 and 15. What is the length of the hypotenuse?

• A. 16
• B. 17
• C. 18
• D. 19
• E. 20

Hint:

The Pythagorean theorem is a quick way to find the hypotenuse in a right triangle: \( a^2 + b^2 = c^2 \). Just make sure to square the legs first, then take the square root to solve for \( c \).

Answer 1

The Correct Option is B

To find the length of the hypotenuse \( c \) of a right triangle, we use the Pythagorean theorem: \[ a^2 + b^2 = c^2, \] where \( a \) and \( b \) are the lengths of the legs, and \( c \) is the hypotenuse. We are given that: \[ a = 8
\text{and}
b = 15. \] Substitute these values into the Pythagorean theorem: \[ 8^2 + 15^2 = c^2. \] Now, square the values of \( a \) and \( b \): \[ 64 + 225 = c^2. \] Add the results: \[ 289 = c^2. \] Now, take the square root of both sides: \[ c = \sqrt{289} = 17. \] Thus, the length of the hypotenuse is \( c = 17 \).