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

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If the perimeter of a rectangular garden plot is 34 feet and  [#permalink]

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New post 05 Jan 2014, 13:10
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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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Re: If the perimeter of a rectangular garden plot is 34 feet and  [#permalink]

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New post 05 Jan 2014, 20:56
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4

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

Sol: Let the length be L and Breadth be B. Given Perimeter 2(L+B)= 34 -----> Thus L+B=17
LB=60------> We can solve the equation but best way will be to plug in.

Note that A and B can be ruled out because the other side will be bigger. So the options are between C, D and E
Let L be 10 Ft then B=7 ft and Area is 70 which is not true
Let L be 12ft then B=5 ft and Area is 60 -----> Bingo...what we need
Ans D
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Re: If the perimeter of a rectangular garden plot is 34 feet and  [#permalink]

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Re: If the perimeter of a rectangular garden plot is 34 feet and  [#permalink]

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New post 05 Jan 2014, 21:37
So, let the length be l and the width be w.

Perimeter = 2(l+w) = 34; l+w = 17;
Area = l * w = 60; w = 60/l;

Sub w in Perimeter;
l+(60/l) = 17
l^2-17l+60=0;
l =5,12

The larger side will be 12.
Ans is (D).
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Re: If the perimeter of a rectangular garden plot is 34 feet and  [#permalink]

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New post 06 Jan 2014, 02:59
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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

Answer is D
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Re: If the perimeter of a rectangular garden plot is 34 feet and  [#permalink]

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New post 06 Jan 2014, 08:54
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  [#permalink]

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New post 06 Jan 2014, 23:46
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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If the perimeter of a rectangular garden plot is 34 feet and  [#permalink]

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New post 17 Jun 2016, 11:40
1
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


GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
1. Please provide your solutions to the questions;
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!



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.
Answer D.

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.
Answer D.
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If the perimeter of a rectangular garden plot is 34 feet and  [#permalink]

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New post 17 Jun 2016, 11:53
1
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

Answer is D


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Re: If the perimeter of a rectangular garden plot is 34 feet and  [#permalink]

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New post 25 Jan 2017, 07:20
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  [#permalink]

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New post 13 Apr 2017, 01:46
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 &nbs [#permalink] 13 Apr 2017, 01:46
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