Question

The area of a rectangle is numerically equal to twice its perimeter and both length and breadth are integers. How many such rectangles are possible?​

Answer 1

Answer:

The area of a rectangle is numerically equal to twice its perimeter and both length and breadth are integers. How many such rectangles are possible?

Step-by-step explanation:

The area of a rectangle is numerically equal to twice its perimeter and both length and breadth are integers

To find : How many such rectangles are possible

Solution:

Length Say Length = L

& Breadth = B

Perimeter = 2(L + B)

Area = LB

LB =  2 * 2(L + B)

=> LB = 4L  + 4B

=> 4L = LB - 4B

=> 4L = B ( L - 4)

=> B = 4L/(L - 4)         or L = 4B/(B - 4)

if  L < 4  as then B will be - ve

=> L > 4   & B > 4  

L = 5

=> B = 20

Perimeter = 50   Area = 100

L = 6  

=> B = 12

Perimeter = 36  Area  = 72

L = 8

=> B = 8

Perimeter = 32   Area = 64

Hence 3 Rectangle Possibles

( 5 , 20)    & ( 6 , 12)  & ( 8 , 8 )

Where area of a rectangle is numerically equal to twice its perimeter

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