A Rectangular Board Has Its Perimeter And Area Equal. Find Out All The Possible Dimensions Of Board

A rectangular board has its perimeter and area equal. Find out all the possible dimensions of board

 

Answer:

The dimensions possible are l >2 units with corresponding width solved using eq 1  

Step-by-step explanation:

A rectangular board has its perimeter and area equal. Find out all the possible dimensions of board.

Let P = perimeter of rectangle

      A = area of rectangle

      l = length

      w = width

Solution:

A = P

A = lw    

P = 2l +2w

lw = 2l + 2w  (eq 1)

find the relationship between l and w from eq 1

lw - 2w = 2l

w( l - 2) = 2l

w = 2l/(l-2)

then create examples/ assumptions:

if l = 1 unit

w = (2)(1) /(1-2) = -2 (not possible since negative)

if l = 2 unit

w = (2)(2)/ (2-2) = 4/0 (not possible since undefined)

if l = 3 unit

w = (2)(3)/ (3-2) = 6 unit (possible)

therefore, the dimensions possible are l >2 units with corresponding width solved using eq 1