Question

A right triangle has the lengths of the legs are 60 centimeters and 80 centimeters. what is the length, in cm, of the hypotenuse?

Answer 1

The following image shows a diagram (not to scale) of the triangle with the indicated measurements:

We will label them as "a" and "b" for reference:

And we need to find the hypotenuse of the triangle, which is the side that is opposite to the 90° angle. We will label the hypotenuse as "c":

To solve the problem we have to us The Pythagorean Theorem:

`c^2=a^2+b^2`

Substituting the values of the legs a and b:

`c^2=60^2+80^2`

Since 60^2=3,600 and 80^2=6,400:

`\begin{gathered} c^2=3,600+6,400 \\ c^2=10,000 \end{gathered}`

Finally, to find the hypotenuse "c", take the square root of both sides of the equation:

`\begin{gathered} \sqrt[]{c^2}=\sqrt[]{10,000} \\ c=\sqrt[]{10,000} \\ c=100 \end{gathered}`

The length of the hypotenuse is 100 cm.

Answer: 100cm