Question

What is the answer lol somebody help me please and thank you !

Answer 1

I'm guessing that you know about 45-45-90 and 30-60-90 triangles.

In 45-45-90 triangles, the legs are in a ratio such that the hypotenuse is
`√(2)` times the legs.

In 30-60-90 triangles, the legs are in a ratio of 1:
`√(3)`:2

In the picture given we have been given a value of the side of the 45-45-90 triangle. We can deduce that the value of the hypotenuse is 9
`√(2)` because of the ratio of the sides of a 45-45-90 triangle.

The 30-60-90 triangle shares the same hypotenuse, and so we now know a value of one of its sides as well. The ratio of the side of value 'x' and the hypotenuse is
`√(3)` : 2

We can create an equation to solve for x using these ratios:

`(√(3) )/(2)` =
`(x)/(9√(2) )`

Cross multiply:

2x = 9
`√(6)`

x =
`(9√(6) )/(2)`

Option C