Question

Solve for x.

Geometric Mean
Middle, Left, Right
How do you solve this?

Answer Choices
A. 39.3
B. 34.5
C. 37.8
D. 35.9
​

Answer 1

`\mathrm{A.\: 39.3}`

Explanation:

Let
`h` represent the height of the two smaller triangles in this figure. Because all three triangles are similar, we can set up the following proportion:

`(33)/(h)=(h)/(y)`, for
`y=x-33`.

We can solve for
`h` using the Pythagorean theorem on the second largest triangle:

`33^2+h^2=36^2,\\h=√(36^2-33^2),\\h=√(207)`.

Now plugging in
`h=√(207)` into our proportion
`(33)/(h)=(h)/(y)`, we can solve for y:
`(33)/(√(207))=(√(207))/(y)`.

Cross-multiply to get:

`33y=207,\\y=(207)/(33),\\y\approx 6.3`.

Since we
`y=x-33, y+33=x`.

Therefore, our answer is:

`x=33+y=33+6.3=\fbox{$\mathrm{A.\: 39.3}$}`.