Answer:
The greatest area of rectangle is:
625 square units.
Step-by-step explanation:
It is given that:
A rectangle of perimeter 100 units has the dimensions as:
50-w on the top and bottom.
and a w on its left side and right side.
i.e. we may say the length of the rectangle is:
50-w
and the width of the rectangle is:
w
Now, we need to find the greatest area of rectangle.
As the area of rectangle is:
A = w(50 - w)=50w-w^2
Now, to find the maximum area we differentiate the Area with respect to the width as:
[tex]\dfrac{dA}{dw}=0\\\\i.e.\\\\50-2w=0\\\\50=2w\\\\w=25[/tex]
Hence, to obtain the maximum area the width of the rectangle is: 25 units.
and that of the length of the rectangle is:
50-25=25 units.
Hence, the dimensions of rectangle in order to obtain the maximum area is:
25 units by 25 units.
So, the area of rectangle is:
[tex]Area=25\times 25\\\\Area=625\ \text{square\ units}[/tex]
Hence, the greatest area of rectangle is:
625 square units.
