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duttsit
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What is the maximum right triangles with legs of length 3 ft 05 Nov 2005, 21:32
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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 :)



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What is the maximum right triangles with legs of length 3 ft Updated on: 05 Nov 2005, 22:31
Originally posted by tank on 05 Nov 2005, 22:01.
Last edited by tank on 05 Nov 2005, 22:31, edited 1 time in total.
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duttsit
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 :)
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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
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What is the maximum right triangles with legs of length 3 ft 05 Nov 2005, 22:02
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duttsit
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 :)
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since 14 is the maximum number here and i can show how to cut to get this number. E it is :wink: . Wait, i'm drawing the solution and post here soon.
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What is the maximum right triangles with legs of length 3 ft 05 Nov 2005, 22:10
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here it is:
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proof.doc [24.5 KiB]
Downloaded 114 times

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duttsit
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What is the maximum right triangles with legs of length 3 ft 05 Nov 2005, 22:19
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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.
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What is the maximum right triangles with legs of length 3 ft 05 Nov 2005, 22:30
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duttsit
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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Ya, luckily in this case, its perfectly divisible.
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What is the maximum right triangles with legs of length 3 ft 06 Nov 2005, 00:26
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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....:roll:




duttsit
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.
Show more
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What is the maximum right triangles with legs of length 3 ft 06 Nov 2005, 00:49
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cool_jonny009
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....:roll:




duttsit
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.
Show more


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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