Question

Hi can someone please help me with these math problems I'm struggling with them! and show the work please

Answer 1

First problem: x = √15

Second problem: x = 6√5 (B)

Third problem: x = 6, y = 12 (A)

Fourth problem: x = 6√2 (C)

Explanation:

We use geometric means as follows:

First problem:

`(3)/(x) = (x)/(5)`

`{x}^(2) = 15`

`x = √(15)`

Second problem:

`(20)/(x) = (x)/(9)`

`{x}^(2) = 180`

`x = √(180) = √(36) √(5) = 6 √(5)`

So B is the correct answer.

Third problem:

We have a 30°-60°-90° triangle.

x = 6, y = 12. So A is the correct answer.

Fourth problem:

We have a right isosceles triangle.

x = 12/√2 = 6√2. So C is the correct answer.