Question

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

Answer 1

Answer:

see below

Step-by-step explanation:

Pythagorean theorem:

$a^2 + b^2 = c^2 \\a = \sqrt{c^2-b^2} \\b = \sqrt{c^2-a^2} \\c = \sqrt{a^2+b^2}$, where c is hypotenuse, a and b are the other 2 sides in triangle

1. $x = \sqrt{9^2-3^2}$  = $\sqrt{81-9} = \sqrt{72} = \sqrt{36*2} = 6\sqrt{2}$

2. $x = \sqrt{18^2-10^2} =\sqrt{324-100} = \sqrt{224} =\sqrt{16*14} =4\sqrt{14}$

3. $x = \sqrt{4^2+14^2} =\sqrt{16+196} =\sqrt{212} =\sqrt{4*53} =2\sqrt{53}$