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# In right triangles ABC and DEF, angle C is equal to angle F. If DE = 3

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Math Expert
Joined: 02 Sep 2009
Posts: 49206
In right triangles ABC and DEF, angle C is equal to angle F. If DE = 3  [#permalink]

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07 Sep 2018, 01:23
00:00

Difficulty:

25% (medium)

Question Stats:

80% (02:35) correct 20% (03:30) wrong based on 30 sessions

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In right triangles ABC and DEF, angle C is equal to angle F. If DE = 3, AB = 4.5, and hypotenuse AC = 7.5, what is the difference of the perimeters of the two triangles?

A. 2.5
B. 5
C. 6
D. 8.5
E. 11

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In right triangles ABC and DEF, angle C is equal to angle F. If DE = 3  [#permalink]

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07 Sep 2018, 08:37
Bunuel wrote:
In right triangles ABC and DEF, angle C is equal to angle F. If DE = 3, AB = 4.5, and hypotenuse AC = 7.5, what is the difference of the perimeters of the two triangles?

A. 2.5
B. 5
C. 6
D. 8.5
E. 11

Between right triangles ABC and DEF,
1) Angle B=Angle E=90
2) Angle C=Angle F
3) Angle A= Angle D (Third angles must be same)

So, right triangles ABC and DEF are similar.

Hence the ratios of corresponding sides are equal.

$$\frac{BC}{EF}=\frac{AC}{DF}=\frac{AB}{DE}$$
Or, $$\frac{BC}{EF}=\frac{7.5}{DF}=\frac{4.5}{3}$$-----------(1)
Or, DF=5

In right angled triangle DEF, DE=3, DF=5. So, EF=$$\sqrt{5^2-3^2}$$=4

From(1), BC=1.5*DF=1.5*5=7.5

So perimeter of triangle ABC-perimeter of triangle DEF
=(AB+BC+AC)-(DE+EF+DF)
=(4.5+6+7.5)-(3+4+5)=18-12=6

Ans. (C)

P.S:- We can solve this problem using scale factor approach. (ratio of the perimeters of two similar triangles is same as the ratio of their corresponding sides)
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Re: In right triangles ABC and DEF, angle C is equal to angle F. If DE = 3  [#permalink]

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07 Sep 2018, 11:55
This is a good question. Time-consuming if the concept is not known.
Re: In right triangles ABC and DEF, angle C is equal to angle F. If DE = 3 &nbs [#permalink] 07 Sep 2018, 11:55
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