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# What is the maximum right triangles with legs of length 3 ft

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Joined: 22 Aug 2005
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What is the maximum right triangles with legs of length 3 ft [#permalink]  05 Nov 2005, 20:32
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What is the maximum right triangles with legs of length 3 ft and 4 ft that can be cut from the rectangular sheet of metal of dimension 7 ft x 12 ft.

(A) 7
(B) 8
(C) 10
(D) 12
(E) 14

time: 3 mins for ans with reasons
Intern
Joined: 01 Jun 2005
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Re: PS: Right within Rectangular [#permalink]  05 Nov 2005, 21:01
duttsit wrote:
What is the maximum right triangles with legs of length 3 ft and 4 ft that can be cut from the rectangular sheet of metal of dimension 7 ft x 12 ft.

(A) 7
(B) 8
(C) 10
(D) 12
(E) 14

time: 3 mins for ans with reasons

Ans is E.

Area of triangle = 1/2 x 3x 4 = 6[Note, since it is a right triangle the lengths are in the ratio 3:4:5. Therefore, 3 or 4 could not be the hypotenuse]

Area of the rect = 12x7 = 84

# of triangles from that sheet = 84/6 = 14

Last edited by tank on 05 Nov 2005, 21:31, edited 1 time in total.
SVP
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Re: PS: Right within Rectangular [#permalink]  05 Nov 2005, 21:02
duttsit wrote:
What is the maximum right triangles with legs of length 3 ft and 4 ft that can be cut from the rectangular sheet of metal of dimension 7 ft x 12 ft.

(A) 7
(B) 8
(C) 10
(D) 12
(E) 14

time: 3 mins for ans with reasons

since 14 is the maximum number here and i can show how to cut to get this number. E it is . Wait, i'm drawing the solution and post here soon.
SVP
Joined: 24 Sep 2005
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here it is:
Attachments

proof.doc [24.5 KiB]

VP
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Wonderful lexieqv/tank. Tank i believe you know that, just dividing area gives maximum number of triangles if "there is no leftover". As lexieqv explained in the doc, there is a way to cut. The latter part is more important in this question.
Intern
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duttsit wrote:
Wonderful lexieqv/tank. Tank i believe you know that, just dividing area gives maximum number of triangles if "there is no leftover". As lexieqv explained in the doc, there is a way to cut. The latter part is more important in this question.

Ya, luckily in this case, its perfectly divisible.
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duttsit,
I also got E by dividing the area....but if there isleft over ..in the sheet is there any formula or trick to get the # of tringle ..? or drawing the figure is the only hope....

duttsit wrote:
Wonderful lexieqv/tank. Tank i believe you know that, just dividing area gives maximum number of triangles if "there is no leftover". As lexieqv explained in the doc, there is a way to cut. The latter part is more important in this question.
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Joined: 24 Sep 2005
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Kudos [?]: 139 [0], given: 0

cool_jonny009 wrote:
duttsit,
I also got E by dividing the area....but if there isleft over ..in the sheet is there any formula or trick to get the # of tringle ..? or drawing the figure is the only hope....

duttsit wrote:
Wonderful lexieqv/tank. Tank i believe you know that, just dividing area gives maximum number of triangles if "there is no leftover". As lexieqv explained in the doc, there is a way to cut. The latter part is more important in this question.

The trick is that: Firstly you cut triangles from the one width and one length, if there's no overleft, there won't be any overleft.
In this case, 12 is divisible by 4 and 3
7= 3+4
For sure, there won't be any overleft when you cut from one width and one length.
In short, as long as length/width( one of the two) is sum of the triangle's two legs AND width/length( one of the two) is the product of the triangle's two legs, there won't be overleft.
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