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605-655 (Medium)|   Geometry|      
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Bunuel
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The perimeter of right triangle DEF is 144 inches. If we connect the m 20 Jul 2020, 03:46
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45% (medium)

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68% (01:49) correct 32% (02:04) wrong based on 122 sessions

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The perimeter of right triangle DEF is 144 inches. If we connect the midpoints of the three sides of DEF, we can form a smaller triangle. What will its perimeter be?

A. 12
B. 36
C. 48
D. 64
E. 72
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E
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The perimeter of right triangle DEF is 144 inches. If we connect the m Updated on: 20 Jul 2020, 05:03
Originally posted by nkme2007 on 20 Jul 2020, 04:23.
Last edited by nkme2007 on 20 Jul 2020, 05:03, edited 1 time in total.
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Bunuel
The perimeter of right triangle DEF is 144 inches. If we connect the midpoints of the three sides of DEF, we can form a smaller triangle. What will its perimeter be?

A. 12
B. 36
C. 48
D. 64
E. 72
Show more

As the triangle is formed using the lines connecting mid-points, the area becomes 1/4 that of the actual area and perimeter becomes 1/2 that of the actual perimeter.

OA: E
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The perimeter of right triangle DEF is 144 inches. If we connect the m 20 Jul 2020, 04:57
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Bunuel
The perimeter of right triangle DEF is 144 inches. If we connect the midpoints of the three sides of DEF, we can form a smaller triangle. What will its perimeter be?

A. 12
B. 36
C. 48
D. 64
E. 72
Show more

Answer: Option E

The check the explanation attached here
Attachments

Screenshot 2020-07-20 at 5.26.35 PM.png
Screenshot 2020-07-20 at 5.26.35 PM.png [ 651.71 KiB | Viewed 3693 times ]

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The perimeter of right triangle DEF is 144 inches. If we connect the m 14 Aug 2020, 09:14
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I noticed a ratio relationship of 144/6sides = (Perimeter small)/3sides

[144/6]=[Psmall/3]
432 = 6x
x = 72
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The perimeter of right triangle DEF is 144 inches. If we connect the m 09 Sep 2020, 14:26
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Bunuel
The perimeter of right triangle DEF is 144 inches. If we connect the midpoints of the three sides of DEF, we can form a smaller triangle. What will its perimeter be?

A. 12
B. 36
C. 48
D. 64
E. 72
Show more
Solution:

Anytime a new triangle is formed by connecting the midpoints of the original triangle, the perimeter of the new triangle will be half the perimeter of the original triangle. Here, since the perimeter of the original triangle is 144 inches, the perimeter of the new triangle is 144/2 = 72 inches.

Answer: E
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The perimeter of right triangle DEF is 144 inches. If we connect the m 12 Sep 2020, 23:13
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Mid-Point Theorem: if you join a Line Segment from the Mid-Point of 1 Side of a Triangle to the Opposite Side's Mid-Point, that Mid-Segment will be

(1) 1/2 the Length of the 3rd Side

and

(2) Parallel to that 3rd Side


Call the 3 Sides of the triangle:

Side EF = D
Side DF = E
Side DE = F


1st) by the Mid-Point Theorem of Triangles: The Line Segment Connecting the Mid-Point of Side F to the Mid-Point of Side D will be = 1/2 * (Length of Parallel Side E)

2nd) Similar Logic, the 2nd Side of the Inner Triangle = 1/2 * (Length of Side D)

3rd) Similar Logic, the 3rd Side of the Inner Triangle = 1/2 * (Length of Side F)

D + E + F = 144

Perimeter of Inner Triangle = 1/2(D) + 1/2(E) + 1/2(F) = ?

-take 1/2 a Common-

1/2 * (D + E + F) = ?

1/2 * (144) = 72 Degrees

-E-
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The perimeter of right triangle DEF is 144 inches. If we connect the m 14 Mar 2023, 07:37
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