The trick is to recognize a few things.
1. These are similar triangles, so the ratio of BU to BC is the same as BT to BA and UT to CA.
[tex]\dfrac{BU}{BC}=\dfrac{BT}{BA}=\dfrac{UT}{CA}[/tex]
2. BC = 2 BUs and BA = 2 BTs
This means the sides of the short triangle are half the length of the sides of the big triangle.
Put in other words, CA = 2 UT
Put into an equation x+29 = 2(x+19).
x + 29 = 2x + 38
–9 = x
So that means UT = 10 and CA = 20
