Padraig has a rectangular vegetable garden bordered by his house on on

Question

Padraig has a rectangular vegetable garden bordered by his house on one side and a picket fence on the three other sides. Currently, Padraig’s house can provide a boundary of up to 50 feet for one side of the garden and he has already used 75% of 96 feet of available picket fence to enclose the other three sides of the garden. If the picket fence can only be arranged in whole foot dimensions, what would be the length of the boundary of the garden bordered by Padraig’s house required to produce the largest possible rectangular vegetable garden should he extend the three other dimensions of it using the remaining feet of picket fence?

Select the length of the garden bordered by the house in feet and largest possible vegetable garden area in square feet after the fence is extended. Make only two selections, one in each column.

Select the length of the garden bordered by the house in feet and largest possible vegetable garden area in square feet after the fence is extended. Make only two selections, one in each column.

Saraskarki · Answer

We are asked to maximize the area of rectangle 
Lets jump to the answer choices
3 choices are available for length of border around the house 
A) 32 Is not possible because it makes the garden a square 
B) 48 then the opposite side is also 48 and hence the other sides are 24 each 
Area= 24*48= 1152 
C) 50 then the opposite side is also 50 and the other sides are 23 each 
Area=23*50=1150 
Side = 48
Area= 1152

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ramiav · Answer

I understand the answer, but the questions is quite bad worded.

--------y---------|-----------|
|  ggggggggggg | 50 H   -|
|  ggggggggggg |_______|
| 50 + x  -gggg- | x
|  ggggggggggg  |
|-------y--------- |

max area (50+x)*y
fence used = 3/4 of 96 = 72
so
50 + 2x + 2y = 72

....

Here the answer

...|--------------y--------------|------|
x | ggggggggggggggggggg |hhhh|
...|--------------y--------------|hhhh|
 ....................................... |hhhh|
 ....................................... ---------

2y+x = 96 ( because 75% is not important as we are still building, who cares about the poles or the neighbors 😅 )
and as x should be <= 50 let put numbers

Area = X * Y
and Y is (96 - X) / 2

so 
X:  32, 48, 50
Y: 32, 24, 23
----------------
1024,  1152 , 1150

hchnr · Answer

let x be the length (where the house boundary at) y be the width of the garden
method: if we have the sum of x and y we can get the maximum of the product (xy)
you can search this on youtube for more details:     Maximum product from two numbers that sum to 18

from the question we know that
2y+x=96
and we want to get the maxi of xy

plug x=96-2y into xy
we have:
xy = 96y-2(y^2)
to get the maxi, we need a   quadratic function,  which looks like f(x) = a(x-b)^2+c 
 this way when x = b, we have c, the constant, as our maxi

thus, 
xy = -2(y^2-48y) = -2(y^2-48y+24^2)+2*24^2 = -2(y-24)^2+1152 (our quadratic function)
i.e. when y = 24, 1152 is the maxi of xy

and when y = 24, x = 48
therefore the answer (48,1152)

Hitesh0701 · Answer

karishma : Can you help me out in this case.
How can we arrive at 24 to be the width of the garden ?

demawtf · Answer

Padraig has a rectangular vegetable garden bordered by his house on one side and a picket fence on the three other sides. Currently, Padraig’s house can provide a boundary of up to 50 feet for one side of the garden and he has already used 75% of 96 feet of available picket fence to enclose the other three sides of the garden. If the picket fence can only be arranged in whole foot dimensions, what would be the length of the boundary of the garden bordered by Padraig’s house required to produce the largest possible rectangular vegetable garden should he extend the three other dimensions of it using the remaining feet of picket fence?

Select the length of the garden bordered by the house in feet and largest possible vegetable garden area in square feet after the fence is extended. Make only two selections, one in each column.

Select the length of the garden bordered by the house in feet and largest possible vegetable garden area in square feet after the fence is extended. Make only two selections, one in each column.

My reasoning was:
- boundary of up to 50 feet for one side
- he has already used 75% of 96 feet of available picket fence to enclose the other three sides of the garden --> so 25% of 96 is available = 24

Max area: if we assume 50 feet and 24, 50*24 =1.200 but it is not in the list of possible values. We have 1152 as maximum to be selected so x*24=1152 --> x=48

Padraig has a rectangular vegetable garden bordered by his house on on

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Length of the garden bordered by the house	Maximum area
		32
		48
		50
		1024
		1150
		1152

GMAT Two-part Analysis (TPA) Questions

Padraig has a rectangular vegetable garden bordered by his house on on

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