In the diagram below, triangle abc ~ triangle dec . What is the value of x? A. 28 b. 24 c. 22 d. 26

Question

asked Sep 20, 2021 64.7k views

2 Answers

Pribina · Answer 1 · 2021-09-25T12:47:37+0000

Answer:

Option A.

Explanation:

From the figure attached,

Given : ΔABC ~ ΔDEC

By the property of similarity,

"Corresponding sides of the similar triangles are proportional"

$\frac{\text{AB}}{ED}=(BC)/(EC)=(AC)/(DC)$

Since,
$\frac{\text{AB}}{ED}=(AC)/(DC)$

(42)/(6)=(x)/((32-x))

6x = 42(32 - x)

6x = 1344 - 42x

6x + 42x = 1344

48x = 1344

x =
(1344)/(48)

x = 28 units

Therefore, Option (A). x = 28 units will be the answer.