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

Question

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) 15 ft

WoundedTiger · Accepted Answer

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

nutshell · Answer

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).

PerfectScores · Answer

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

kinjiGC · Answer

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)

AKG1593 · Answer

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

bimalr9 · Answer

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.

LogicGuru1 · Answer

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

Ndkms · Answer

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.

diegocml · Answer

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

Perimeter:  2L+2W=34\ 2\left( L+W ight) =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 ight) =60\ 17L-{ L }^{ 2 }=60\ { L }^{ 2 }-17L+60=0\ \left( L-5 ight) \left( L-12 ight) =0\ L=5,\quad L=12

The length of the longer side is 12.

ArnauG · Answer

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).

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

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