It takes a while to see through this one.
I think that's because the triangle is in a weird position.

The arrows on the two across-lines tell us that those lines are parallel.
And THAT tells us that the two triangles are similar ... the whole big triangle,
and the smaller triangle on the bottom.

If two triangles are similar, then what ?

-- Their corresponding angles are equal. That doesn't help us in this problem.

-- Their corresponding sides are in the same ratio. That helps us a lot !

The left side of the big triangle = 5 + 8 = 13
The left side of the small triangle = 8

Now we know that corresponding sides of the two triangles
have the ratio of 13 to 8 .

The right side of the big triangle = 4 + x
The right side of the small triangle = x

The ratio has to be 13/8 , so ===> (4+x) / x = 13 / 8 .

That's the tough part. Now you take it and finish it off from here.

8 0

3 years ago