A right triangle has legs of length 5 inches and 12 inches. What is the length, in inches,… — ACT

A right triangle has legs of length $5$ inches and $12$ inches. What is the length, in inches, of the hypotenuse of this triangle?

Answer: 13 inches

The length of the hypotenuse is 13 inches.

The Pythagorean theorem states that in any right triangle with legs

a

and

b

and hypotenuse

c

a^2 + b^2 = c^2

. Substituting the given values:

5^2 + 12^2 = 25 + 144 = 169

. Taking the square root of

169

gives the hypotenuse length of

13

Identify the lengths of the two legs.

a = 5

b = 12

These are the given side lengths perpendicular to each other.

Apply the Pythagorean theorem

a^2 + b^2 = c^2

5^2 + 12^2 = 25 + 144 = 169

To find the square of the hypotenuse.

Solve for the hypotenuse

c

by taking the square root.

c = \sqrt{169} = 13

To find the side length of the hypotenuse.

Pythagorean Theorem

Question