Question

Find the exact length of the third side.

Answer 1

`√(5)` or 2.236

Explanation:

The pythagorem theorm states that side 1^2 + side^2 = hypotenuse^2

2^2 + 1^2 = h^2

4+1 = h^2

5 = h^2

`√(5) = \sqrt{h^(2) }`

`√(5) =h`

Answer 2

The third side is sqrt(5)

Explanation:

This is a right triangle so we can use the Pythagorean theorem

a^2+b^2 = c^2 where a and b are the legs and c is the hypotenuse

We know the legs are 1 and 2 and we are looking for the hypotenuse.

1^2+2^2 = c^2

1+4 = c^2

5 =c^2

Take the square root of each side

sqrt(5) = sqrt(c^2)

sqrt(5) =c

The third side is sqrt(5)