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655-705 (Hard)|   Geometry|      
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Bunuel
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What is the maximum number of right triangles with legs of length 3 ft 25 Jun 2019, 03:52
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65% (hard)

Question Stats:

45% (01:19) correct 55% (01:46) wrong based on 110 sessions

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What is the maximum number of right triangles with legs of length 3 ft and 4 ft that can be cut from the rectangular sheet of metal represented in the figure attached?

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

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217695.18.gmc74207s.gif
217695.18.gmc74207s.gif [ 1.43 KiB | Viewed 3277 times ]
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What is the maximum number of right triangles with legs of length 3 ft Updated on: 26 Jun 2019, 08:24
Originally posted by Apt0810 on 26 Jun 2019, 03:46.
Last edited by Apt0810 on 26 Jun 2019, 08:24, edited 1 time in total.
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Below figure is showing all 14 triangles which can be formed:
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IMG_20190626_161410__01.jpg
IMG_20190626_161410__01.jpg [ 1.41 MiB | Viewed 2878 times ]

IMG_20190626_161410__01.jpg
IMG_20190626_161410__01.jpg [ 1.41 MiB | Viewed 2887 times ]

IMG_20190626_161410.jpg
IMG_20190626_161410.jpg [ 2.63 MiB | Viewed 2966 times ]

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What is the maximum number of right triangles with legs of length 3 ft 25 Jun 2019, 23:13
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chetan2u Bunuel Should we just figure of the area of the rectangle (7*12=84) and area of the required triangle (1*3*4/2=6) and arrive at the triangles 84/6=14 or should we check if such triangles are possible from the balance area say : first can you cut all the area of the rectangle in right angles triangles of the required measurements? or some area will be unusable?
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What is the maximum number of right triangles with legs of length 3 ft 26 Jun 2019, 02:33
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Arvind42
chetan2u Bunuel Should we just figure of the area of the rectangle (7*12=84) and area of the required triangle (1*3*4/2=6) and arrive at the triangles 84/6=14 or should we check if such triangles are possible from the balance area say : first can you cut all the area of the rectangle in right angles triangles of the required measurements? or some area will be unusable?
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its fine either way, because there is no unusable area
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What is the maximum number of right triangles with legs of length 3 ft 26 Jun 2019, 02:41
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farharajeev
Arvind42
chetan2u Bunuel Should we just figure of the area of the rectangle (7*12=84) and area of the required triangle (1*3*4/2=6) and arrive at the triangles 84/6=14 or should we check if such triangles are possible from the balance area say : first can you cut all the area of the rectangle in right angles triangles of the required measurements? or some area will be unusable?




its fine either way, because there is no unusable area
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But how do we determine that there is no unusable area?. This question it might work but others?

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What is the maximum number of right triangles with legs of length 3 ft 26 Jun 2019, 08:23
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Bunuel

What is the maximum number of right triangles with legs of length 3 ft and 4 ft that can be cut from the rectangular sheet of metal represented in the figure attached?

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

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Attachment:
217695.18.gmc74207s.gif
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area of ∆ = 1/2 * 3*4 ; 6
area of rectangle ; 7*12 ; 84
so max fig which can be cut ; 84/6 ; 14
IMO E
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What is the maximum number of right triangles with legs of length 3 ft 28 Jun 2019, 05:32
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Rather than 3-4-5 triangle, Let's consider a rectangle with sides 3 and 4. Each rectangle can be further cut into 2 triangles.

Along the base 7:

Placing rectangle with side 3 cm will stack up 3 rectangles in height: 12/4= 3

Now, along base 7: on remaining 4 cm, we can stack up 4 rectangles: 12/3= 4.

Total 4x3 rectangles: 7
Therefore, total triangles: 14

Ans E

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