Question

Does anyone know this I’m struggling to figure this out

Answer 1

Answer:

$\frac{ \sqrt{6} }{3}$

Step-by-step explanation:

To find side x , since it the shortest side. Divide the second longest side by sqr root of 3.

Why?

This is a 30-60-90 triangle so that means the second longest side will be sqr root of 3 times more than the shortest side

$\sqrt{2} \div \sqrt{3}$

$\frac{ \sqrt{2} }{1} \times \frac{1}{ \sqrt{3} } = \frac{ \sqrt{2} }{ \sqrt{3} }$

RATIONALIZE the denominator

$\frac{ \sqrt{2} }{ \sqrt{3} } \times \frac{ \sqrt{3} }{ \sqrt{3} } = \frac{ \sqrt{6} }{3}$

Sqr root of 6 over 3 is the answer.

This section is extra If you want to.

Since the longest side is twice the shortest side, the longest side is

$\frac{2 \sqrt{6} }{3}$

Let proof

using pythagorean theorem,

$( \frac{ \sqrt{6} }{3} ) {}^{2} + (\sqrt{2} ) {}^{2}$

$\frac{6}{9} + 2 = \frac{24}{9}$

$\sqrt{ \frac{ {24} }{9} } = \frac{2 \sqrt{6} }{3}$

So it is right.