Question

15 in. 12 in. b what is the perimeter? if necessary, round to the nearest tenth. inches

Explanation:

Step1: Find the length of \( b \) using Pythagorean theorem

The Pythagorean theorem for a right triangle is \( a^2 + b^2 = c^2 \), where \( c \) is the hypotenuse, and \( a, b \) are the legs. Here, \( c = 15 \) in, \( a = 12 \) in, so we solve for \( b \):
\( b^2 = c^2 - a^2 \)
\( b^2 = 15^2 - 12^2 \)
\( b^2 = 225 - 144 \)
\( b^2 = 81 \)
\( b = \sqrt{81} = 9 \) in.

Step2: Calculate the perimeter

Perimeter of a triangle is the sum of all sides: \( \text{Perimeter} = 15 + 12 + 9 \)
\( \text{Perimeter} = 36 \) in.

Answer:

36