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The figure shows a square patio surrounded by a walkway of width x [#permalink]

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30 Jun 2005, 20:03

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The figure shows a square patio surrounded by a walkway of width x meters. If the area of the walkway is 132 square meters and the width of the patio is 5 meters greater than the width of the walkway, what is the area of the patio, in square meters?

The figure shows a square patio surrounded by a walkway of [#permalink]

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24 Oct 2008, 03:46

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The figure shows a square patio surrounded by a walkway of width x meters. If the area of the walkway is 132 square meters and the width of the patio is 5 meters greater than the width of the walkway, what is the area of the patio, in square meters?

A. 56 B. 64 C. 68 D. 81 E. 100

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Hi LiveStronger, nice way to solve it. could you please explain me how do you go from step 1 to step 2. It took me 3 lines of operations and you can do it in just one. I definitely need to be faster in the exam so this kind of tips will be really useful. thks!!

Hi LiveStronger, nice way to solve it. could you please explain me how do you go from step 1 to step 2. It took me 3 lines of operations and you can do it in just one. I definitely need to be faster in the exam so this kind of tips will be really useful. thks!!

The solutions above subtract the inner square from the outer one, which is a good approach. One other way to get to the same answer: divide up the patio. You have the four corners, measuring x by x, and four rectangles lined up with each side of the inner square which measure x by x+5. So:

4x^2 + 4x(x+5) = 132 2x^2 + 5x = 33

etc.
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The figure shows a square patio surrounded by a walkway of width x meters. If the area of the walkway is 132 square meters and the width of the patio is 5 meters greater than the width of the walkway, what is the area of the patio, in square meters?

A. 56 B. 64 C. 68 D. 81 E. 100

width of the walkway = x width of the patio = x+5 = x+5 width of the whole area = x+5+x = 3x+5

(3x+5)^2 - (x+5)^2 = 132 9x^2 + 30x + 25 - x^2 -10x -25 = 132 8x^2 + 20x = 132 4 (2x^2 + 5x) = 132 2x^2 + 5x - 33 = 0 2x^2 + 11x - 6x - 33 = 0 x (2x+11) -3 (3x +11) = 0 (x-3) (2x+11) = 0 x = 3 or -11/2 but -11/2 is not possible as length/width cannot be in -ve. so x = 30

so area of the patio = (3+5)^2 = 64
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If its convenient, u can also attempt backsolving it:- On first glance A,C are clearly out. (E) 100 means side of patio is 10 so width of walkway =5. the walkway has 4 rectangles 2 among them are each 20*5=100 --impossible for total of 132. (D) 81 means side of patio is 9 so width of walkway =4. the walkway has 4 rectangles 2 among them are each 17*4=68. 2 such rectangles account for 136--hence impossible for total of 132. (C) 64 means side of patio is 8 so width of walkway =3. the walkway has 4 rectangles 2 among them are each 14*3=42 and rest are 8*24.total= 2(42+24)=132.

the width of the patio is X + 5 and the width of the big square is 3X +5, therefore the are of the big square is equal to the area of the walkway plus the area of the patio, the equation is (3X +5)^2 -132 = (X + 5)^2, X = 3 or X = -11/2 since the width of the patio = X+5 = 3 + 5 =8 the area equals to 8^ 2 =64 hope it helps!!

The figure shows a square patio surrounded by a walkway of width x meters. If the area of the walkway is 132 square meters and the width of the patio is 5 meters greater than the width of the walkway, what is the area of the patio, in square meters?

A. 56 B. 64 C. 68 D. 81 E. 100

Smaller square=Patio Let the side of Patio be "s". Width of walkway=x width of the patio is 5 meters greater than the width of the walkway(Actually it should be "side of the patio is 5 meters greater than the width of the walkway" because patio is a square)

So, \(s=x+5\)

If we see the figure properly, the outer quadrilateral is also a square with side \(s+x+x\) OR \(x+5+x+x=3x+5\)

We know, the area of the walkway is 132 square meters:

Area of walkway=Area of outer square-Area of inner square Area of walkway=(3x+5)^2-(x+5)^2=132

Re: The figure shows a square patio surrounded by a walkway of width x met [#permalink]

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10 Nov 2011, 12:48

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The algebraic solution to the problem is given below:

Given, Width of walkway = x Width of Patio = Width of Walkway + 5 meters = x+5 meters Area of walkway = 132 square meters

From the given figure, we know that the width of the square figure i.e. Patio + Walkway will be: 2 times the width of walkway + width of Patio i.e 2(x) + (x+5) = 3x+5

Therefore, the area of this combined figure (square) will be (3x+5)^2

Now, the area of the walkway will be equal to the difference between the area of the combined figure and the square Patio i.e. (3x+5)^2 - (x+5)^2 This is given to be 132 square meters.

Therefore, expanding and simplifying the equation, (3x+5)^2 - (x+5)^2 = 132 We get, 8x^2 + 20x - 132 = 0 i.e. 2x^2 + 5x - 33 = 0 Solving the above quadratic equation will yield the value of x as -6.5 and 3. Since the width of the walkway can't be negative, the value of x is 3 meters.

Using this, we can calculate the area of the Patio, which is (x+5)^2 i.e. (3+5)^2 = 8^2 = 64 square meters.

This is option B.

Hope this helps

Cheers!
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Re: The figure shows a square patio surrounded by a walkway of [#permalink]

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04 Jul 2015, 06:57

amitdgr wrote:

The figure shows a square patio surrounded by a walkway of width x meters. If the area of the walkway is 132 square meters and the width of the patio is 5 meters greater than the width of the walkway, what is the area of the patio, in square meters?

A. 56 B. 64 C. 68 D. 81 E. 100

Hi bunuel,

Could you please provide your comments on how we are getting 5+3x.

The figure shows a square patio surrounded by a walkway of width x meters. If the area of the walkway is 132 square meters and the width of the patio is 5 meters greater than the width of the walkway, what is the area of the patio, in square meters?

A. 56 B. 64 C. 68 D. 81 E. 100

Hi bunuel,

Could you please provide your comments on how we are getting 5+3x.

i didnt get it.

Thanks.

It is given that width of the patio is 5 more than width of the walkway. Now, walkway's 'extension on either side of the patio' is 'x' and thus width of the of the patio = \(W_P\) = 5+x

Now, total width of the walkway = \(W_W\) = width of the patio + 2*x = 5+x+2x = 5+3x
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