In the figure below, triangle ABC and triangle FDE are similar. If the

Question

In the figure below, triangle ABC and triangle FDE are similar. If the lengths of the sides are indicated in units, how many units long is DE ?

(A) 25
(B) 28
(C) 30
(D) 32
(E) 40

Attachment:

2021-01-15_14-02-39.png [ 29.1 KiB | Viewed 2106 times ]

D

GMATinsight · Answer

OBSERVATION 1: Ratio of corresponding sides are equal in case of similar triangles

OBSERVATION 2: Sides opposite to smallest angle is smallest and side opposite to largest angle is largest

So, ratio of sides should be

\frac{16}{20} = \frac{24}{30} = \frac{?}{40}

i.e.  ? = 32

Answer:Option D

TarunKumar1234 · Answer

Given, 24/x = 30/40 or, x = 32. So, It is D.

BrushMyQuant · Answer

↧↧↧ Weekly Video Solution to the Problem Series ↧↧↧

https://www.youtube.com/watch?v=VwA7HQ6k2m4

Theory: If Two Triangles are Similar then their sides will be in the same ratio

Given that △ ABC and △ FDE are similar

=> Their corresponding sides will be in the same ratio

=>  \frac{AB}{FD}  =  \frac{BC}{DE}  =  \frac{AC}{FE}

=>  \frac{30}{24}  =  \frac{40}{DE}

=> DE =  \frac{40*24}{30}  = 32

So,  Answer will be D 
Hope it helps!

Watch the following video to learn the Basics of Similar Triangles

https://www.youtube.com/watch?v=n3THKzTq5ZM

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