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# Find the area of the rectangle ABCD, if the length and breadth are odd

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Find the area of the rectangle ABCD, if the length and breadth are odd  [#permalink]

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14 Apr 2019, 07:29
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45% (medium)

Question Stats:

68% (02:02) correct 32% (02:09) wrong based on 41 sessions

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Find the area of the rectangle ABCD, if the length and breadth are odd positive integers.

(1) The perimeter of rectangle ABCD = 28 cm

(2) The area of the square whose side length is equal to the length of the rectangle, is 80% greater than the area of the rectangle.
Math Expert
Joined: 02 Aug 2009
Posts: 8261
Re: Find the area of the rectangle ABCD, if the length and breadth are odd  [#permalink]

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14 Apr 2019, 08:00
Find the area of the rectangle ABCD, if the length and breadth are odd positive integers.

(1) The perimeter of rectangle ABCD = 28 cm
l and b can be 7 and 7 or 9 and 5 or 11 and 3 and so on

(2) The area of the square whose side length is equal to the length of the rectangle, is 80% greater than the area of the rectangle.
So $$l^2=1.8(l*b)...l=1.8b$$. No values

Combined..
l is integer, so 1.8b has to be an integer, so B has to be a multiple of 5..
l can be 1.8*5=9 or 1.8*10=18..
Only 9 is possible, so l*b=5*9=45

C
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Re: Find the area of the rectangle ABCD, if the length and breadth are odd  [#permalink]

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14 Apr 2019, 08:20
themindful wrote:
Find the area of the rectangle ABCD, if the length and breadth are odd positive integers.

(1) The perimeter of rectangle ABCD = 28 cm

(2) The area of the square whose side length is equal to the length of the rectangle, is 80% greater than the area of the rectangle.

#1
2*(l+b)=28
l+b=14
l,b= 11,3; or 13,1
insufficient
#2
area of square = l^2 = 1.8*(l*b)
or say ; l = 1.8b ; since value are integers so we can say l=2b
insufficient
from 1 & 2
3b=14
b= 14/3 ; 4.6 ~ 5
so l = 14-5 ; 9
sufficient ; IMO C l = 9 & b= 5
Re: Find the area of the rectangle ABCD, if the length and breadth are odd   [#permalink] 14 Apr 2019, 08:20
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