Answer:
Assuming the length to be x and the width to be y.
Since the area is 64cm, hence
x*y = 64 (equation 1)
Since the perimeter is 40cm, hence
x + x + y + y = 40
2x + 2y = 40
2(x + y) = 2(20)
x + y = 20 (equation 2)
Hence by using simultaneous equation,
x = 20 - y (equation 3)
Substituting equation 3 into equation 1, we get
(20-y)*y=64
20y-y^2=64
Tidying up the equation,
y^2 - 20y + 64 = 0
By using factorisation,
(y-16)(y-4)=0
y=16 or y=4
By substituting y=16 into equation 1,
x*16=64
x = 4
By substituting y = 4 into equation 1,
x*4=64
x=16
Therefore,
The length is 4 cm while the width is 16 cm.
OR
The length is 16 cm while the width is 4cm.
Hope this helps!!
