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# If the perimeter of a rectangular garden plot is 34 feet and its area

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Re: If the perimeter of a rectangular garden plot is 34 feet and its area [#permalink]
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If the perimeter of a rectangular garden plot is 34 feet and its area is 60 square feet, what is the length of each of the longer sides?

(A) 5 ft
(B) 6 ft
(C) 10 ft
(D) 12 ft
(E) 15ft

A very good contender for back solving. Lets label the column and start with C.

Length of a side.......Length of other side...Perimeter
(A) 5 ft
(B) 6 ft
(C) 10 ft................60/10 = 6.......................2(6+10) = 32 (This was supposed to be 34 however it is a lesser number so we move down towards bigger number)
(D) 12 ft................60/12= 5 .......................2(12 + 5) = 34 (BINGO!)
(E) 15ft

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Re: If the perimeter of a rectangular garden plot is 34 feet and its area [#permalink]
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

If the perimeter of a rectangular garden plot is 34 feet and its area is 60 square feet, what is the length of each of the longer sides?

(A) 5 ft
(B) 6 ft
(C) 10 ft
(D) 12 ft
(E) 15ft

Difficulty : Sub 600

Perimeter of the rectangle = 2(L+B) where L : length and B : breadth.
so L+B = 17
Area of rectangle is L*B = 60
And also L > B
Now check options and Option D) satisfies all the above condition . Option D)
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Re: If the perimeter of a rectangular garden plot is 34 feet and its area [#permalink]
Perimeter of a rectangle=2(l+b)=34
=> l+b=17
or, b=17-l
Now,area of rectangle=l x b=60
=> l x (17-l)=60
or, l x (17-l)=12 x 5
l=12 ft.
Ans:D
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Re: If the perimeter of a rectangular garden plot is 34 feet and its area [#permalink]
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Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

If the perimeter of a rectangular garden plot is 34 feet and its area is 60 square feet, what is the length of each of the longer sides?

(A) 5 ft
(B) 6 ft
(C) 10 ft
(D) 12 ft
(E) 15ft

Problem Solving
Question: 24
Category: Geometry; Algebra Perimeter; Area; Simultaneous equations
Page: 65
Difficulty: 550

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Conditions to satisfy. (GIVEN)
$$l*b = 60$$
$$2(l+b) = 34$$

LCM of 60 = $$2*2*3*5$$
Our answer choices include 5,6,10, 12 and 15.

taking,
$$l = 2*2*3$$ and $$b= 5$$ satisfy both the conditions.

Another approach.

Easiest thing to do here is using the answer choices to solve the problem.
We know that of the given answer choices one is our answer.
If we take 10 as the longest length, then the breadth(b) has to be 6. This satisfies l*b=60 but it doesn't satisfies 2(l+b) =34.
If we take 12 as our length then breadth will be 5, as 12 * 5 = 60. Also, 2(12+5)= 34.
Therefore, longest length is 12.
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Re: If the perimeter of a rectangular garden plot is 34 feet and its area [#permalink]
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The question will essentially transform into a quadratic equation with the following expression :-
$$x^2-17x+60=0$$
or (x-5)(x-12)=0
so x=5,12
The longest side will be 12 and the shorter side will be 5

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Re: If the perimeter of a rectangular garden plot is 34 feet and its area [#permalink]
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I think the 550 underestimates the difficulty of the question. In my opinion is 600 because of the time constrains.

Strictly speaking, in GMAT terms, the right answer is not only the one that gives you the right solution but also the one that works faster.

Within the the first 10-20 seconds is obvious that there is a quadratic down the road and the process of solving quadratics in gmat can be very hairy. On the other side I feel back solving is the optimum solution.
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Re: If the perimeter of a rectangular garden plot is 34 feet and its area [#permalink]
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Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

If the perimeter of a rectangular garden plot is 34 feet and its area is 60 square feet, what is the length of each of the longer sides?

(A) 5 ft
(B) 6 ft
(C) 10 ft
(D) 12 ft
(E) 15ft

If we let L be the length and W be the width:

Perimeter: $$2L+2W=34\\ 2\left( L+W \right) =34\\ L+W=17$$

Area: $$LW=60$$

We can manipulate the perimeter to $$W=17-L$$ and then replace it in the area formula.

$$L\left( 17-L \right) =60\\ 17L-{ L }^{ 2 }=60\\ { L }^{ 2 }-17L+60=0\\ \left( L-5 \right) \left( L-12 \right) =0\\ L=5,\quad L=12$$

The length of the longer side is 12.
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Re: If the perimeter of a rectangular garden plot is 34 feet and its area [#permalink]
We are given the perimeter of a rectangular garden plot as 34 feet and its area as 60 square feet.

Using the formula for perimeter, 2L + 2W = 34, we can simplify it to L + W = 17.

The formula for area, L * W = 60, allows us to express W in terms of L as W = 17 - L.

Substituting this into the area equation, we get L * (17 - L) = 60.

Simplifying further, we have the quadratic equation L^2 - 17L + 60 = 0.

By factoring, we find (L - 5)(L - 12) = 0.

The possible values for L are L = 5 and L = 12.

Since we're looking for the length of each of the longer sides, we choose the larger value, L = 12.

Therefore, the length of each of the longer sides is 12 feet, corresponding to option (D).
Re: If the perimeter of a rectangular garden plot is 34 feet and its area [#permalink]
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