Question

The hypotenuse of a right triangle is 7 inches, and one of the legs is the square root of thirteen inches. Find the length of the other leg.

Answer 1

By using the well-known Pythagorian theorem we can write this equation:
7^2=13+b^2 -> b^2=49-13=36
The square root of 36 is obviously 6.
So, the other leg has a length of 6 inches :)

Answer 2

The length of the other leg is
`6in.`

Explanation:

It was given that, the hypotenuse of the triangle is
`7in.` and one of the legs is
`√(13)in.`.

We want to find the length of the other leg.

Let the length of the other leg be
`l\:in.`.

We now apply the Pythagoras Theorem to obtain;

`l^2+(√(13)) ^(2) =7^2`

`\Rightarrow l^2+13 =49`

`\Rightarrow l^2=49-13`

`\Rightarrow l^2=36`

We take the positive square root of both sides to get;

`\Rightarrow l=√(36)`

`\Rightarrow l=6\:in.`

See diagram in attachment.