Question:
A right triangle has one leg of 5 cm and a hypotenuse of 13 cm. What is the length of the other leg?
A right triangle has one leg of 5 cm and a hypotenuse of 13 cm. What is the length of the other leg?
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Use the Pythagorean theorem \( a^2 + b^2 = c^2 \) to find the missing side of a right triangle, where \( a \) and \( b \) are the legs and \( c \) is the hypotenuse.
Updated On: Oct 6, 2025
- \( 10 \, \text{cm} \)
- \( 12 \, \text{cm} \)
- \( 15 \, \text{cm} \)
- \( 14 \, \text{cm} \)
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The Correct Option is B
Solution and Explanation
Step 1: Use the Pythagorean theorem. Let the length of the other leg be \( x \). According to the Pythagorean theorem:
\[
5^2 + x^2 = 13^2.
\]
Step 2: Simplify the equation:
\[
25 + x^2 = 169.
\]
Step 3: Subtract 25 from both sides:
\[
x^2 = 144.
\]
Step 4: Take the square root of both sides:
\[
x = 12.
\]
Thus, the length of the other leg is \( 12 \, \text{cm} \).
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