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

Question

https://gmatclub.com/forum/download/file.php?id=50469 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 2019-09-21_1822.png

BrentGMATPrepNow · Accepted Answer

Let's add a line to divide the figure into   3 separate shapes  
 https://i.imgur.com/5aVaZGF.png

( area of blue triangle ) + ( area of red rectangle ) + ( area of green rectangle ) = 10,800
 Area of triangle = (base)(height)/2 
So, we get:  (x)(96)/2  +  4x  +  (4)(100)  = 10,800
Simplify:  48x  +  4x  +  400  = 10,800
Simplify: 52x + 400 = 10,800
Subtract 400 from both sides to get: 52x = 10,400
Solve: x = 10,400/52 = 200

Answer: A

Cheers,
Brent

Archit3110 · Answer

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

CareerGeek · Answer

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

ScottTargetTestPrep · Answer

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

Answer: A

menonpriyanka92 · Answer

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

dabaobao · Answer

x = ?

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

ANSWER: A

2020prep2020 · Answer

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

Fdambro294 · Answer

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

KVKool · Answer

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

Michele4 · Answer

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

BrentGMATPrepNow · Answer

Your equation (for the area of a triangle) represents a shape that's different from the given diagram. 
 https://i.imgur.com/KSFjwyY.png

ScottTargetTestPrep · Answer

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.

Bambi2021 · Answer

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

Saharakj · Answer

Can someone tell me why I can't use trapezoid formula to calculate (x+4)(4+100)/2=10800 x=207-4=203 please

Crater · Answer

It is close to being a trapezium, but still if you check closely it has 5 sides instead of 4.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards