Question

What is the length of the hypotenuse of a right triangle if the two other sides are of lengths 2 and 16?

Answer 1

`c=2sqrt65`

Explanation:

Use the Pythagorean theorem, `c^2=a^2+b^2`, where `c` is the hypotenuse, and `a` and `b` are the other two sides.

Let side `a=2` and side `b=16`.

Substitute the given values into the equation.

`c^2=2^2+16^2`

Simplify.

`c^2=4+256`

Simplify.

`c^2=260`

Take the square root of both sides.

`c=sqrt260`

Determine the prime factors of `260`.

`c=sqrt(2xx2xx5xx13)`

Group identical factors.

`c=sqrt((2xx2)xx5xx13)`

Rewrite `(2xx2)` as `2^2`.

`c=sqrt(2^2xx5xx13)`

Apply the square root rule `sqrt(a^2)=a`.

`c=2sqrt(5xx13)`

Simplify.

`c=2sqrt65`