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A square piece of sailcloth is trimmed by 4 feet on one edge to form a [#permalink]
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chetan2u wrote:
draditya wrote:
A square piece of sailcloth is trimmed by 4 feet on one edge to form a rectangular piece, which is then cut in half to create two triangular sails. If the area of each of the sails is 240 square feet, what was the perimeter of the original piece of sailcloth?


A) 75 feet

B) 88 feet

C) 96 feet

D) 104 feet

E) 576 feet


area of each triangle=1/2 * x * (x-4)=240..
x=24.. so perimeter = 24*4=96
C

Please follow the fig.
Attachment:
square.png
square.png [ 3.21 KiB | Viewed 4255 times ]

area of triangle=1/2*x*(x+4)=240
x=20
so side of square =20+4=24
perimeter 24*4=96
Ans C
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Re: A square piece of sailcloth is trimmed by 4 feet on one edge to form a [#permalink]
Is there a way to calculate fast x(x-4)=480?

please help!
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Re: A square piece of sailcloth is trimmed by 4 feet on one edge to form a [#permalink]
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Expert Reply
JoaquinCerda wrote:
Is there a way to calculate fast x(x-4)=480?

please help!


Number properties can get you to answer fast

1) Both x and x-4 have the same property of being odd or even. Since product is even, both are even.
2) One of the two x or x-4 must be multiple of 10.
Now we have to just test numbers in which x or x-4 is a multiple of 10.
10*6 or 10*14....No
20*16=320...No
20*24=480...yes
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Re: A square piece of sailcloth is trimmed by 4 feet on one edge to form a [#permalink]
chetan2u wrote:
JoaquinCerda wrote:
Is there a way to calculate fast x(x-4)=480?

please help!


Number properties can get you to answer fast

1) Both x and x-4 have the same property of being odd or even. Since product is even, both are even.
2) One of the two x or x-4 must be multiple of 10.
Now we have to just test numbers in which x or x-4 is a multiple of 10.
10*6 or 10*14....No
20*16=320...No
20*24=480...yes


Ohhh!! thank you very much for the explanation!!!!!
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Re: A square piece of sailcloth is trimmed by 4 feet on one edge to form a [#permalink]
Expert Reply
draditya wrote:
A square piece of sailcloth is trimmed by 4 feet on one edge to form a rectangular piece, which is then cut in half to create two triangular sails. If the area of each of the sails is 240 square feet, what was the perimeter of the original piece of sailcloth?


A) 75 feet

B) 88 feet

C) 96 feet

D) 104 feet

E) 576 feet

Solution:

Let the side of the original square be x feet. Thus, the dimensions of the rectangle after the square is trimmed are x and (x - 4). We can create the equation based on the area of one of the triangular pieces into which the rectangle was cut :

1/2 * x * (x - 4) = 240

x^2 - 4x = 480

x^2 - 4x - 480 = 0

(x + 20)(x - 24) = 0

x = -20 or x = 24

Since x can’t be negative, x = 24. Therefore, the perimeter of the original square was 4 * 24 = 96 feet.

Answer: C
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Re: A square piece of sailcloth is trimmed by 4 feet on one edge to form a [#permalink]
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