Question

I think it's a 30 60 90 special triangle to find x but I need help!​

Answer 1

The value of x is $10 \sqrt{3}$.

Solution:

Given image is a right triangle.

Hypotenuse = 30

Part 1 = 20

Part 2 = Hypotenuse - Part 1

          = 30 - 20

Part 2 = 10

Leg = x

Leg rule of geometric mean theorem:

$\frac{\text { hypotenuse }}{\text { leg }}=\frac{\text{leg}}{\text { part of its leg}}$

$\Rightarrow \frac{30}{x}=\frac{x}{10}$

Do cross multiplication.

$\Rightarrow 30\times 10=x\times x$

$\Rightarrow 300=x^2$

$\Rightarrow 10^2 \times 3=x^2$

Taking square root on both sides, we get

$\Rightarrow 10 \sqrt{3}= x$

The value of x is $10 \sqrt{3}$.