The perimeter of square S and rectangular R are equal,if the sides of r are in the ratio 2:3,what is the ratio of the region R to the area of region S?
1)25:16
2)24:25
3)5:6
4)4:5
5)4:9
plz help me solve this sum
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The perimeter of square S and rectangular R are equal,if the sides of r are in the ratio 2:3,what is the ratio of the region R to the area of region S?
Perimter of square = 4*S
Perimater of rectangle = 2(l+b)
Both the perimeters are equal
=> 4*S = 2(l+b)
Since, the 2 sides of R are in the ratio 2:3
l = 2*k and b = 3*k
=> 4* S = 2(2*k + 3*k)
=> 4* S = 2(5 *k)
=> 4* S = 10* K
=> S = 5/2 * K
ratio of the region R to the area of region S?
Area of rectangle R = l*b
Area of square S = S ^2
R:S = l*b: s^2
= (2* k) *(3*k) : (5/2 * k) ^2
= 6 * k^2 : 25/4 * k^2
= 6:25/4
multiply both by 4
= 6 * 4 : 25/4 * 4
= 24: 25
Perimter of square = 4*S
Perimater of rectangle = 2(l+b)
Both the perimeters are equal
=> 4*S = 2(l+b)
Since, the 2 sides of R are in the ratio 2:3
l = 2*k and b = 3*k
=> 4* S = 2(2*k + 3*k)
=> 4* S = 2(5 *k)
=> 4* S = 10* K
=> S = 5/2 * K
ratio of the region R to the area of region S?
Area of rectangle R = l*b
Area of square S = S ^2
R:S = l*b: s^2
= (2* k) *(3*k) : (5/2 * k) ^2
= 6 * k^2 : 25/4 * k^2
= 6:25/4
multiply both by 4
= 6 * 4 : 25/4 * 4
= 24: 25
- AleksandrM
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At what level of difficulty is this problem?
It took me almost 3 minutes to brainstorm it and carefully write out the arithmetic to avoid making a stupid mistake.
It took me almost 3 minutes to brainstorm it and carefully write out the arithmetic to avoid making a stupid mistake.
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Well guys, I think GMAT is about choosing the right answer, not spending time in finding algebric solutions.
How I did it......
We know that for a given perimeter, the square is the geometric form that maximize the area. So the ratio between a rectangle and square with the same perimeter must be less than 1. Eliminate 1), which is greater.
Then by picking numbers, for instance 2 and 3 for the sides of the rectangle one will find that the ratio must be very close to 1 (0,9....).
The only choice so close to 1 is 24/25.
I took me 1,5min.
IMO is a 600 level question.
How I did it......
We know that for a given perimeter, the square is the geometric form that maximize the area. So the ratio between a rectangle and square with the same perimeter must be less than 1. Eliminate 1), which is greater.
Then by picking numbers, for instance 2 and 3 for the sides of the rectangle one will find that the ratio must be very close to 1 (0,9....).
The only choice so close to 1 is 24/25.
I took me 1,5min.
IMO is a 600 level question.
- AleksandrM
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I just saw why my answer took so long, I was too focused on using algebra.
When I used a faster method, I solved this problem in a little over a minute.
since the ratio of the sides of the rectangle are in the form of 2:3, then you can just assume the following:
4s = 2(3) + 2(6)
4s = 10
s = 10/4
Then the ratio of areas will be:
(2)(3)/(10/4)^2 =
6/100/16, which can be reduced to 6/25/4 = 24/25.
This is certainly an easy problem. I need to prevent myself from getting carried away with algebra.
When I used a faster method, I solved this problem in a little over a minute.
since the ratio of the sides of the rectangle are in the form of 2:3, then you can just assume the following:
4s = 2(3) + 2(6)
4s = 10
s = 10/4
Then the ratio of areas will be:
(2)(3)/(10/4)^2 =
6/100/16, which can be reduced to 6/25/4 = 24/25.
This is certainly an easy problem. I need to prevent myself from getting carried away with algebra.
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perimeter of square = perimeter of rectangle
and rectangle sides are in ratio 2:3
by applying numbers to it,
if we take rectangle sides 2 & 3
rectangle perimeter = 10 that would make each square sides 2.5
so used a more convienient numbers 4 & 6 for rectangle sides
that makes each side of aquare as 5 , that gives the area ratio between them as 24:25
and rectangle sides are in ratio 2:3
by applying numbers to it,
if we take rectangle sides 2 & 3
rectangle perimeter = 10 that would make each square sides 2.5
so used a more convienient numbers 4 & 6 for rectangle sides
that makes each side of aquare as 5 , that gives the area ratio between them as 24:25