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The perimeter of right triangle DEF is 144 inches. If we connect the m

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Re: The perimeter of right triangle DEF is 144 inches. If we connect the m [#permalink]
I noticed a ratio relationship of 144/6sides = (Perimeter small)/3sides

[144/6]=[Psmall/3]
432 = 6x
x = 72
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Re: The perimeter of right triangle DEF is 144 inches. If we connect the m [#permalink]
GMATinsight wrote:
Bunuel wrote:
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

The check the explanation attached here

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How to solve this when one doesn't come up with the appropriate side lengths? I sketched the same triangle but got stuck on how to calculate the length of the hypothenuse as I did not know how to come up with the side lengths of the larger triangle.
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Re: The perimeter of right triangle DEF is 144 inches. If we connect the m [#permalink]
Bunuel wrote:
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

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.

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Re: The perimeter of right triangle DEF is 144 inches. If we connect the m [#permalink]
1
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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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Re: The perimeter of right triangle DEF is 144 inches. If we connect the m [#permalink]
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Re: The perimeter of right triangle DEF is 144 inches. If we connect the m [#permalink]
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