Question

A rectangle is 64 cm long 40 cm wide find is area and perimeter​

Answer 1

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!!