Question

How do you find the third side of a right triangle if the base is x = 20m, and height is y = 20m?

Answer 1

The third side is the hypotenuse, which is `20sqrt 2"m"`.

This is an example of an iscoseles right triangle, in which the angles are 45-45-90 degrees. In an iscoseles right triangle, the base and height are the same. The hypotenuse is the missing side and is equal to `"L"sqrt2`, where `"L"` refers to either of the other two legs, which are equal. Therefore, the length of the hypotenuse is `20sqrt 2"m"`.

We can use the Pythagorean theorem to prove this: `c^2=a^2+b^2`. Let side `x=a=20"m"` and side `y=b=20"m"`. The hypotenuse is `c`.

`c^2=(20"m")^2+(20"m")^2` =

`c^2=400"m"^2+400"m"^2`

`c^2=800"m"^2"`

`c=sqrt(800"m"^2)` =

`c=sqrt(20xx20xx2xx"m"^2)` =

`c=20sqrt2"m"`