Question

The legs of a right triangle are 5 units and 15 units. What is the length of the hypotenuse

Answer 1

To find the length of a hypotenuse, we use the Pythagoras Theorem.

`a^2 + b^2 = c^2`
Where we know the side lengths (A , B)

`5^2 + 15^2 = c^2`
And c is the hypotenuse length :)

Answer 2

The lenght of the hypotenuse is
`√(250)` units or
`15.811` units.

Explanation:

We are going to use the Pythagorean theorem to solve this.

The Pythagorean theorem states that given a right triangle in which ''a'' and ''b'' are the length of the legs and ''c'' is the length of the hypotenuse, this three lengths satisfy the following equation :

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

To find the length of the hypotenuse in this exercise, we need to replace the values
`a=5units` and
`b=15units` in the equation and then find the value of c that satisfy it ⇒

`(5units)^(2)+(15units)^(2)=c^(2)`

`25(units)^(2)+225(units)^(2)=c^(2)`

`250(units)^(2)=c^(2)`

Given that
`c>0` ⇒

`c=\sqrt{250(units)^(2)}`

`c=√(250)units`

or
`c=15.811units`