Question

In a rectangle abcd, ab < 65. If ab + bc + cd = 100, what is the maximum possible area of abcd?

Answer 1

Answer:

Step-by-step explanation:

let ab=x and bc=y

area= x.y

x+x+y = 100

2x+y =100

y=100-2x

area = x.(100-2x)

area = 100x-2x²

to maximize, differentiating

d/dx (100x-2x²) = 100-4x=0

100=4x

x=25

y = 100-2×25

y=100-50

y=50

area=25×50=1250