Suppose the length of the triangle is x, if the perimeter of the rectangle is 100 ft, the width of the rectangle will be (50-x) ft.
Area of rectangle will be:
A=length*width
A=x(50-x)
A=50x-x^2
at maximum area, dA/dx=0
thus
dA/dx=50-2x=0
solving for x we get
2x=50
x=25
thus for maximum area length=25 ft
the size of the width will be
50-x=50-25=25 ft
thus the maximum area will be:
25*25=625 sq. feet

5 0

2 years ago

How do the lateral and total surface area of a cylinder differ ?

vichka [17]

The lateral surface area of a cylinder is just the long side connecting the bases, whereas the total surface area includes both the lateral surface area and area of the two circular bases.

$SA_l_a_t=2 \pi rh$ (Imagine a rectangle with the circumfrence of the base as one side and the height as the other being folded around)

$SA = 2 \pi rh + 2 \pi r^2$ (Plus the area of two circles)

The literal difference between surface areas would be the two bases 2πr² if you need that.

8 0

2 years ago