Question

Angle FEG is similar to triangle IHJ. Find the value of X.

Answer 1

`x = 14.8`

Explanation:

As these triangles are similar, every side and angle corresponds and this is key to calculating this equation.

First, look at the side that is labeled
`x + 8` and find the corresponding side on the other triangle. Write this out as a fraction as shown below. Now find two corresponding sides that are both marked (the base lines) and write them out as a fraction as well (note that which ever triangle you are solving for, it's numbers will go on the top of the fraction)

`(x + 8)/(36) = (38)/(60)`

We want to get the
`x` by its self and at the moment it is divided by 36. To remove the 36, we need to multiply both sides of the equation by 36

36 x
`(x + 8)/(36) = (38)/(60)` x 36

This cancels out both the 36s on the left leaving us with

`x + 8 = (38)/(60)` x 36

all that needs to happen now is to remove the +8 so we are just left with
`x`. to do this, just subtract 8 from both sides and we are left with

`x = (38)/(60)` x 36 - 8

calculate 38 ÷ 60 x 36 - 8 = 14.8

∴
`x = 14.8`

I hope this was helpful and not too long :-)