Question:
A right triangle has legs of lengths 8 and 15. What is the length of the hypotenuse?
A right triangle has legs of lengths 8 and 15. What is the length of the hypotenuse?
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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 \( c \).
Updated On: Oct 6, 2025
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The Correct Option is B
Solution and Explanation
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 \( c = 17 \).
\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 \( c = 17 \).
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