Question

In the following exercises, use the Pythagorean Theorem to find the length of the hypotenuse.

Short answer

The length of the hypotenuse is$26$.

Step-by-step solution

Step 1. Given Information

We are given a right angled triangle whose lengths of two legs are $24$and $10$.

We need to find the length of the hypotenuse of the triangle.

Step 2. Concept used

The Pythagorean Theorem states that in any right triangle, $a^2+b^2=c^2$where $c$is the length of the hypotenuse and $a$and $b$are the lengths of the legs.

Step 3. Find the hypotenuse

As the two legs are of length $24$and $10$. So in the equation $a^2+b^2=c^2$substitute $24$for $a$and $10$for $b$.

$\begin{array}{rcl}{24}^2+{10}^2& =& c^2\\ 576+100& =& c^2\\ 676& =& c^2\end{array}$

Taking square root both sides we get

$\begin{array}{rcl}\sqrt{676}& =& \sqrt{c^2}\\ 26& =& c\end{array}$

So the length of the hypotenuse is $26$.