Question

The legs of a right triangle measure `2sqrt3` and `5`. What is the length of the hypotenuse?

Answer 1

`sqrt37`

Explanation:

Pythagoras theorem gives us the equation:

`a^2 + b^2 = c^2` where `c` is the hypotenuse and `a,b` are the two legs.

Substitute the value of the two legs in.

`(2sqrt3)^2 + 5^2 = c^2`

`12 + 25 = c^2`

`c^2 = 37`

`c=sqrt37`

Normally, when you take the square root of a square the answer should be `+-`. However, a length can't be a negative, so `sqrt37` is the only solution.