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

Answer:

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

Step-by-step explanation:

It was given that, the hypotenuse of the triangle is $7in.$ and one of the legs is $\sqrt{13}in.$.

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;

$l^2+(\sqrt{13}) ^{2} =7^2$

$\Rightarrow l^2+13 =49$

$\Rightarrow l^2=49-13$

$\Rightarrow l^2=36$

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

$\Rightarrow l=\sqrt{36}$

$\Rightarrow l=6\:in.$

See diagram in attachment.

Answer 2

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 :)