Question

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

Answer 1

Answer:

Length = 49.5 unit and width = 49.5 unit

Step-by-step explanation:

Given as , Perimeter of rectangle = 198 unit

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

Or,                                   198 = 2 ×  (Length + width)

Or,                                   $\frac{198}{2}$ = 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)$\frac{D(99w - w^2)}{Dw}$ = 0         as, constant diff is 0

So, 99 - 2w = 0

Or, w = $\frac{99}{2}$

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