The hypotenuse of a right triangle measures 13 inches, and one of its legs measures 5 inch… — Armed Services Vocational Aptitude Battery (ASVAB)

The hypotenuse of a right triangle measures $13$ inches, and one of its legs measures $5$ inches. What is the length of the other leg?

The length of the other leg is

12

inches.

The correct answer is found by properly substituting the hypotenuse (

13

) and the known leg (

5

) into the Pythagorean theorem (

a^2 + b^2 = c^2

). Rearranging to solve for the missing leg gives

a^2 = 13^2 - 5^2

, which simplifies to

a^2 = 169 - 25 = 144

. Taking the square root of

144

yields

12

Set up the Pythagorean theorem equation (

a^2 + b^2 = c^2

) with the given values.

a^2 + 5^2 = 13^2

The Pythagorean theorem relates the two legs (

a

and

b

) to the hypotenuse (

c

) of a right triangle.

Square the known numerical values.

a^2 + 25 = 169

Evaluating the exponents is the first operational step in solving the equation.

Isolate the variable term

a^2

by subtracting

25

from both sides.

a^2 = 144

This leaves the squared variable isolated on one side of the equation.

Take the square root of both sides to find the length of the leg.

a = 12

The square root is the inverse operation of squaring, yielding the final length.

The Pythagorean theorem (

a^2 + b^2 = c^2

) can be rearranged to find a missing leg by subtracting the square of the known leg from the square of the hypotenuse (

a^2 = c^2 - b^2

Question