In a right triangle, the two shorter sides (legs) measure 10 inches and 24 inches. What is… — Armed Services Vocational Aptitude Battery (ASVAB)

In a right triangle, the two shorter sides (legs) measure $10$ inches and $24$ inches. What is the length of the hypotenuse in inches?

The length of the hypotenuse is 26 inches.

The hypotenuse is found by applying the Pythagorean theorem (

a^2 + b^2 = c^2

). When you square the given legs (

10

and

24

), you get

100

and

576

. Adding these gives

676

. Finally, taking the square root of

676

results in

26

. This is also recognized as a scaled version of the fundamental 5-12-13 Pythagorean triple (multiplied by 2).

Recall the Pythagorean theorem formula.

a^2 + b^2 = c^2

This formula connects the lengths of the legs (

a

and

b

) to the hypotenuse (

c

) in a right triangle.

Substitute the given leg lengths into the formula.

10^2 + 24^2 = c^2

The lengths of the two shorter sides are given as 10 and 24.

Square the lengths of the legs.

100 + 576 = c^2

Following the order of operations, evaluate the exponents before adding.

Add the squared values together.

676 = c^2

Combine the values to find the square of the hypotenuse.

Take the square root of both sides to solve for c.

c = \sqrt{676} = 26

Taking the square root provides the final length of the hypotenuse.

Pythagorean Theorem

Question