Question

Solve for x. Can you please help me?

Answer 1

Answer:

6√3

Step-by-step explanation:

Let's take the vertical side in the middle as y and the side on the left as z.

We have:

from the right triangle on the right:

9²+y²=x²

from the right triangle over the big triangle:

z²+x²=(9+3)²=12²

from the right triangle on the left:

3²+y²=z²

We can use substitution in our three equations to get x.

9²+y²=x²

z²+x²=12²

3²+y²=z²

First, solve for y² in terms of x². We want everything in terms of x so we can solve for it.

9²+y²=x²

subtract 9² from both sides

x²-81 = y²

plug that into the third equation

3²+(x²-81)=z²

x²-72=z²

z²+x²=144 (the second equation)

plug x²-72 for z²

x²-72+x² = 144

add 72 to both sides

2x² =216

divide both sides by 2 to isolate x²

x²=108

square root both sides to get x

x = √108 = 6√3