A square piece of sailcloth is trimmed by 4 feet on one edge to form a

Question

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

A) 75 feet

B) 88 feet
 
C) 96 feet
 
D) 104 feet
 
E) 576 feet

chetan2u · Answer

area of each triangle=1/2 * x * (x-4)=240..
x(x-4)=240*2=480
Immediate observations 
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
x=24.. 
OR
 x^2-4x=480.....x^2-4x-480=0....x^2-24x+20x-480=0.....(x-24)(x+20)=0 
So x can be -20 or 24. But x has to be positive, so x=24
so perimeter = 24*4=96
C

EMPOWERgmatRichC · Answer

Hi draditya,

This question can be solved with a standard 'math' approach or it can be solved by TESTing THE ANSWERS.

We're given a number of facts to work with:
1) We start with a SQUARE piece of cloth.
2) We cut 4 feet off of one edge (and for a rectangle)
3) That rectangle is cut diagonally to form two sails (with area of 240 ft^2 each).

We're asked for the ORIGINAL PERIMETER of the cloth.

Let's TEST Answer B: 88 feet
If...
Perimeter = 88 feet
Dimensions = 22 by 22

Rectangle dimensions = 18 x 22
Triangle area = (1/2)(18)(22) = 198 ft^2 This is TOO SMALL.
Eliminate Answers A and B.

Let's TEST Answer D: 104 feet
If....
Perimeter = 104 feet
Dimensions = 26 by 26

Rectangle dimensions = 22 x 26
Triangle area = (1/2)(22)(26) = 286 ft^2 This is TOO BIG.
Eliminate Answers D and E.

There's only one answer left...

Final Answer:  C

GMAT assassins aren't born, they're made,
Rich

rohit8865 · Answer

Please follow the fig. square.png area of triangle=1/2*x*(x+4)=240 x=20 so side of square =20+4=24 perimeter 24*4=96 Ans C

JoaquinCerda · Answer

Is there a way to calculate fast x(x-4)=480?

please help!

chetan2u · Answer

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

JoaquinCerda · Answer

Ohhh!! thank you very much for the explanation!!!!!

ScottTargetTestPrep · Answer

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

A square piece of sailcloth is trimmed by 4 feet on one edge to form a

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