Question

Find the unknown side length. Write your answer in simplest radical form.

Answer 1

see below

Explanation:

Pythagorean theorem:

`a^2 + b^2 = c^2 \\a = √(c^2-b^2) \\b = √(c^2-a^2) \\c = √(a^2+b^2)`, where c is hypotenuse, a and b are the other 2 sides in triangle

1.
`x = √(9^2-3^2)` =
`√(81-9) = √(72) = √(36*2) = 6√(2)`

2.
`x = √(18^2-10^2) =√(324-100) = √(224) =√(16*14) =4√(14)`

3.
`x = √(4^2+14^2) =√(16+196) =√(212) =√(4*53) =2√(53)`