Apel Sinoman has 100 ft of fencing material to enclose a rectangular exercise run for her dog. One side of the run will border her house, so she will only need to fence three sides. What dimensions will give the enclosure the maximum area?

For maximum area of the rectangular exercise run dimensions will be 50ft by 25ft.

Step-by-step explanation:

Let the length of the rectangular exercise run = l ft

and width of the run = w ft

Sinoman has to cover a rectangular exercise run from three sides with the fencing material,

So length of the material = (l + 2w) ft

l + 2w = 100

l = 100 - 2w --------(1)

Area of the rectangular area covered = Length × width

A = lw

A = w(100 - 2w)    [(l = 100 - 2w)from equation (1)

For maximum area we find the derivative of area and equate it to zero.

A' = 100 - 4w

For A' = 0

100 - 4w = 0

4w = 100

w = 25 ft

From equation (1)

l = 100 - 2w

l = 100 - 2×(25)

l = 50 ft

Therefore, for maximum area of the rectangular exercise run dimensions will be 50ft by 25ft.

care to share were the trapezoid shown is ?