Question

ABCD∼EFGH AD=45 in. , EH=75 in. , and AB=30 in. What is EF ?

Answer 1

EF = 50 in.

In similar figures, corresponding sides are proportional.  We use the similarity statement ABCD~EFGH to write a proportion:

$\frac{AB}{EF}=\frac{AD}{EH} \\ \\ \frac{30}{x}=\frac{45}{75}$

Cross multiply the proportion:
45*x = 75*30
45x = 2250

Divide both sides by 45:
45x/45 = 2250/45
x = 50