Question

What is the correct answer for this

Answer 1

The measure of length a is 21

Explanation:

ΔABC ~ ΔDBE

I use equation :

`\ \: \: \: \: \: \: \: \: \: \: \: \: (ab)/(bd) = (bc)/(be) \\ \: \: \: (36 + 18)/(18) = (a + 42)/(a) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: (54)/(18) = (a + 42)/(a) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 3 = (a+42)/(a)\\ \: \: \: \: \: \: \: \: \: \: \: \: \: 3a = a + 42 \\ \: \: \: \: \: \: 3a - a = 42 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: 2a = 42 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: a = (42)/(2) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: a = 21`

So, the measure of length a is 21

Hope it helpful and useful :)