Question

In the diagram below, AABC~ ADEC. What is the value of x?

Answer 1

Answer:

x = 6

Step-by-step explanation:

It's given that triangles ABC & DEC are similar . Hence their corresponding similar sides will be proportional to each other.

$= > \frac{ab}{de} = \frac{bc}{ce} = \frac{ac}{dc}$

$= > \frac{ab}{de} = \frac{21}{7} = \frac{24 - x}{x}$$= > \frac{24 - x}{x} = \frac{21}{7}$

$= > \frac{24 - x}{x} = \frac{21}{7}$

$= > \frac{24 - x}{x} = 3$

$= > 24 - x = 3x$

$= > 4x = 24$

$= > x = \frac{24}{4} = 6$

Answer 2

Since ∆ABC ~ ∆DEC, we may write :

AB/DE = BC/EC = AC/DC

That is, AC/DC = BC/EC ........(1)

Put down the respective lengths in Eq(1),

(24-x)/x = 21/7

24*7 - 7x = 21x

28x = 168

x = 6

There hence, the value of x is 6.