The hypotenuse of a right triangle is 15 centimeters long. One leg is 9 cm long. How do you find the length of the other leg?

2 Answers
Mar 22, 2018

The other leg is "12 cm" long.

Explanation:

Use the Pythagorean theorem:

c^2=a^2+b^2,

where:

c is the hypotenuse, and a and b are the other two sides (legs).

Let a="9 cm"

Rearrange the equation to isolate b^2. Plug in the values for a and c, and solve.

b^2=c^2-a^2

b^2=("15 cm")^2-("9 cm")^2

Simplify.

b^2="225 cm"^2-81 "cm"^2"

b^2="144 cm"^2"

Take the square root of both sides.

b=sqrt("144 cm"^2")

Simplify.

b="12 cm"

Mar 22, 2018

12 centimeters long.

Explanation:

Since this is a right triangle, we can use the Pythagorean Theorem.

![https://www.onlinemathlearning.com/http://pythagorean-theorem.html](https://useruploads.socratic.org/yddUfckQ0We097UVMQGA_displayImage.aspx.jpg)
"c = hypotenuse"
"a = leg"
"b = leg"

We can substitute in c (the hypotenuse) and a (one of the legs) to find the length of b (the other leg)
a^2 + b^2 = c^2
9^2 + b^2 = 15^2
81 + b^2 = 225
b^2 = 144
b = sqrt144
b = 12

So the other leg is 12 centimeters long.