The value of x is [tex]10 \sqrt{3}[/tex].
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:
[tex]$\frac{\text { hypotenuse }}{\text { leg }}=\frac{\text{leg}}{\text { part of its leg}}[/tex]
[tex]$\Rightarrow \frac{30}{x}=\frac{x}{10}[/tex]
Do cross multiplication.
[tex]$\Rightarrow 30\times 10=x\times x[/tex]
[tex]$\Rightarrow 300=x^2[/tex]
[tex]$\Rightarrow 10^2 \times 3=x^2[/tex]
Taking square root on both sides, we get
[tex]\Rightarrow 10 \sqrt{3}= x[/tex]
The value of x is [tex]10 \sqrt{3}[/tex].
