Question

Anyone know this geometry question?

Answer 1

I'd start by recognizing that the smaller triangle, at the top, is similar to the larger (whole) triangle.

Then:

 a              b
------- = ---------
15+a     20+b

Then 20a + ab = 15b + ab.  Subtract ab from both sides.  We then get 20a = 15b.  Note also that 

 40         b
----- = ----------
 60       b+20

so that 40b + 800 = 60b, or 800 = 20b, or b = 40.

If b = 40, then we can find a from the relationship 20a = 15b found earlier.  With b=40, 20a = 15(40) = 600, so a = 30

a = 30
b= 40