Question

In the triangle, angles ABC and ADE are right angles. If AC = 35, AE = 11, and BE = 10, then what is AD?

Answer 1

The answer is 6.6

Answer 2

Triangles $ABC$ and $ADE$ share angle $A$ and $\angle ADE = \angle ABC$ are both right, so $\triangle ABC\sim \triangle ADE$. From this similarity, we have $\frac{AD}{EA}=\frac{AB}{AC}$. Substituting in the values that are given gives us $\frac{AD}{11}=\frac{10+11}{35}$, so that $AD=\frac{11\cdot 21}{35}=\frac{11\cdot 3}{5}=\boxed{\frac{33}{5}}$.