(1 point) Find the length L and width W (with W≤L) of the rectangle with perimeter 100 that has maximum area, and then find the maximum area.

Width = 25

Length = 25

Area = 625

Step-by-step explanation:

The perimeter of a rectangle is given by the sum of its four sides (2L+2W) while the area is given by the product of the its length by its width (LW). It is possible to write the area as a function of width as follows:

The value of W for which the derivate of the area function is zero is the width that yields the maximum area:

With the value of the width, the length (L) and the area (A) can be also be found:

Since the values satisfy the condition W≤L, the answer is:

Width = 25

Length = 25

Area = 625

207/8 is the right

113.1

step-by-step explanation:

v=4

3πr3=4

3·π·33≈113.09734