Question

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?

Answer 1

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"`

Answer 2

`12` centimeters long.

Explanation:

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

`"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.