Question

What is the dimension of a rectangle if the perimeter is 198

Answer 1

Length = 49.5 unit and width = 49.5 unit

Explanation:

Given as , Perimeter of rectangle = 198 unit

so ,as Perimeter of rectangle = 2× ( Length + width)

Or, 198 = 2 × (Length + width)

Or,
`(198)/(2)` = length + width

So, length + width = 99 unit

Now to make area maximum

Length × width = maximum

Or, (99 - width ) × width = maximum

99 Width - width² = maximum Let width = W

Now differentiate both side with respect to W

D(99W - W²)
`(D(99w - w^2))/(Dw)` = 0 as, constant diff is 0

So, 99 - 2w = 0

Or, w =
`(99)/(2)`

Or, w = 49.5 unit and L = 99- 4905 = 49.5 unit Answer