Question

What are the steps to solving this problem?​

Answer 1

`\large\boxed{B)\ 256}`

Explanation:

Look at the picture.

ΔABC and ΔBDC are similar (AA). Therfore the sides are in proportion:

`(AC)/(CB)=(CB)/(DC)`

We have

AC = x + 144

CB = 240

DC = 144

Substitute:

`(x+144)/(240)=(240)/(144)` cross multiply

`144(x+144)=(240)(240)\qquad\text{divide both sides by 144}\\\\x+144=400\qquad\text{subtract 144 from both sides}\\\\x=256`