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# The figure above shows some of the dimensions of a triangular plaza wi

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Re: The figure above shows some of the dimensions of a triangular plaza wi [#permalink]
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gmatt1476 wrote:

The figure above shows some of the dimensions of a triangular plaza with an L-shaped walk along two of its edges. If the width of the walk is 4 feet and the total area of the plaza and walk together is 10,800 square feet, what is the value of x ?

A. 200
B. 204
C. 212
D. 216
E. 225

PS22502.01

Attachment:
2019-09-21_1822.png

We see that the vertical side of the plaza is 4 feet less than 100, or 96 feet. Therefore, the area of the plaza is ½ * x * 96 = 48x square feet. The area of the walkway is 4(x + 100) = 4x + 400 square feet. Since the total area of the plaza and the walkway is 10,800 square feet, we can create the equation:

48x + 4x + 400 = 10,800

52x = 10,400

x = 200

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The figure above shows some of the dimensions of a triangular plaza wi [#permalink]
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menonpriyanka92 wrote:
Hi All,
Can somebody please explain why we can't approach it the following way:
Area of plaza+walk = 1/2 *(x+4)*100 = 10800
Hence x = 216

Because the plaza + walk is not a triangle but a figure composed of two rectangles and triangle
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Michele4 wrote:
ScottTargetTestPrep BrentGMATPrepNow IanStewart may I ask you why in this specific case 1/2*(x+4)*100= 10800 DOES NOT work?

Your equation (for the area of a triangle) represents a shape that's different from the given diagram.
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Re: The figure above shows some of the dimensions of a triangular plaza wi [#permalink]
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gmatt1476 wrote:

The figure above shows some of the dimensions of a triangular plaza with an L-shaped walk along two of its edges. If the width of the walk is 4 feet and the total area of the plaza and walk together is 10,800 square feet, what is the value of x ?

A. 200
B. 204
C. 212
D. 216
E. 225

PS22502.01

Attachment:
2019-09-21_1822.png

Total area = 1/2*x*(100-4) + x*4 + 100*4
--> 10,800 = 48x + 4x + 400
--> 52x = 10400
--> x = 200

IMO Option A

Pls Hit kudos if you like the solution
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Re: The figure above shows some of the dimensions of a triangular plaza wi [#permalink]
total area of the ∆ plaza = 100 -4 * x/2 = 48x
and the area of the rectangular part ; (x+4)*(4)+(96)*4 = 4x+400
total area ; 52x+400= 10800
x= 200
IMO A

gmatt1476 wrote:

The figure above shows some of the dimensions of a triangular plaza with an L-shaped walk along two of its edges. If the width of the walk is 4 feet and the total area of the plaza and walk together is 10,800 square feet, what is the value of x ?

A. 200
B. 204
C. 212
D. 216
E. 225

PS22502.01

Attachment:
2019-09-21_1822.png
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Re: The figure above shows some of the dimensions of a triangular plaza wi [#permalink]
gmatt1476 wrote:

The figure above shows some of the dimensions of a triangular plaza with an L-shaped walk along two of its edges. If the width of the walk is 4 feet and the total area of the plaza and walk together is 10,800 square feet, what is the value of x ?

A. 200
B. 204
C. 212
D. 216
E. 225

PS22502.01

Attachment:
2019-09-21_1822.png

x = ?

48 x + 4x + 4*100 = 10,800
52x = 10400
x = 200

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Re: The figure above shows some of the dimensions of a triangular plaza wi [#permalink]
Area of Plaza = Area of Right Triangle + Area of 4 by 4 Square formed in the Corner + Area of Vertical Rectangle 4 by 96 + Area of Horizontal Rectangle 4 by X

Vertical Leg of Right Triangle = 100 - 4 width of Walkway = 96

10,800 = 1/2 * (96*x) + 4^2 + 4*96 + 4*X

10,800 = 48x + 400 + 4x

10,400 = 52x

x = 200 Answer Choice A
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Re: The figure above shows some of the dimensions of a triangular plaza wi [#permalink]
2020prep2020 wrote:
menonpriyanka92 wrote:
Hi All,
Can somebody please explain why we can't approach it the following way:
Area of plaza+walk = 1/2 *(x+4)*100 = 10800
Hence x = 216

Because the plaza + walk is not a triangle but a figure composed of two rectangles and triangle

However, it does look like a right angled traingle.
And so combined area of whole figure taken any which way (either by considering as a big traingle or by considering as 3 separate figures) should be same only right?

Posted from my mobile device
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The figure above shows some of the dimensions of a triangular plaza wi [#permalink]
gmatt1476 wrote:

The figure above shows some of the dimensions of a triangular plaza with an L-shaped walk along two of its edges. If the width of the walk is 4 feet and the total area of the plaza and walk together is 10,800 square feet, what is the value of x ?

A. 200
B. 204
C. 212
D. 216
E. 225

PS22502.01

Attachment:
2019-09-21_1822.png

ScottTargetTestPrep BrentGMATPrepNow IanStewart may I ask you why in this specific case 1/2*(x+4)*100= 10800 DOES NOT work?
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Re: The figure above shows some of the dimensions of a triangular plaza wi [#permalink]
Michele4 wrote:
gmatt1476 wrote:

The figure above shows some of the dimensions of a triangular plaza with an L-shaped walk along two of its edges. If the width of the walk is 4 feet and the total area of the plaza and walk together is 10,800 square feet, what is the value of x ?

A. 200
B. 204
C. 212
D. 216
E. 225

PS22502.01

Attachment:
2019-09-21_1822.png

ScottTargetTestPrep BrentGMATPrepNow IanStewart may I ask you why in this specific case 1/2*(x+4)*100= 10800 DOES NOT work?

Response:

That is the formula for the area of a triangle with a base of x + 4 and a height of 100. Had the plaza together with the walk formed a triangle, your technique would work. However, notice that the plaza together with the walk is not a triangle because of the 4 feet side on the top of the figure, and the 4 feet side on the left.
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The figure above shows some of the dimensions of a triangular plaza wi [#permalink]
I thought of it as a big rectangle minus a triangle that complements the plaza to form that rectangle.

100(x+4) - 96x/2 = 10800

200x + 800 - 96x = 21600

x = 200
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The figure above shows some of the dimensions of a triangular plaza wi [#permalink]
Can someone tell me why I can't use trapezoid formula to calculate
(x+4)(4+100)/2=10800
x=207-4=203
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Re: The figure above shows some of the dimensions of a triangular plaza wi [#permalink]
Saharakj wrote:
Can someone tell me why I can't use trapezoid formula to calculate
(x+4)(4+100)/2=10800
x=207-4=203