Question

This is Geometry. Can someone help me find the side length asked for?

Answer 1

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.

    $\dfrac{BU}{BC}=\dfrac{BT}{BA}=\dfrac{UT}{CA}$

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