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

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Bunuel
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In the figure below, triangle ABC and triangle FDE are similar. If the [#permalink] New post   15 Jan 2021, 06:30
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A
B
C
D
E

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5% (low)

Question Stats:

88% (01:23) correct 12% (02:24) wrong based on 73 sessions
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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

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2021-01-15_14-02-39.png
2021-01-15_14-02-39.png [ 29.1 KiB | Viewed 1659 times ]
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D
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In the figure below, triangle ABC and triangle FDE are similar. If the [#permalink] New post   15 Jan 2021, 07:03
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Bunuel wrote:
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

Show Spoiler
Attachment:
2021-01-15_14-02-39.png


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
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TarunKumar1234
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Re: In the figure below, triangle ABC and triangle FDE are similar. If the [#permalink] New post   15 Jan 2021, 08:40
Given, 24/x = 30/40 or, x = 32.

So, It is D. :)
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In the figure below, triangle ABC and triangle FDE are similar. If the [#permalink] New post   14 Jan 2023, 02:51
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↧↧↧ Weekly Video Solution to the Problem Series ↧↧↧




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

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gmatclubot
In the figure below, triangle ABC and triangle FDE are similar. If the [#permalink]
14 Jan 2023, 02:51
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