contestada

a rectangular playground is to be fenced off and divided into two parts by a fence parallel to one side of the playground. 360 feet of fencing is used. find the dimensions of the playground that will enclose the greatest total area. a) 110 by 70 feet with the divider 70 feet long b) 90 by 90 feet with the divider 90 feet long c) 85 by 65 feet with the divider 86 feet long d) 90 by 60 feet with the divider 60 feet long e) 100 by 70 feet with the divider 100 feet long

Respuesta :

the dimensions of the playground that will enclose the greatest total area is 90*90 = 8100 feet

Let the length of the playground is L and width is W.

Perimeter = 2 (L + W)

360 = 2 (L + W)

L + W = 180   ... (1)

Area, A = L x W

A = L (180 - L)

A = 180 L - L²

differentiate with respect to L.

dA / dL = 180 - 2 L

Put it equal to zero for maxima and minima

180 - 2L = 0

L = 90 feet

W = 180 - 90 = 90 feet

learn more about of rectangle here

https://brainly.com/question/15711863

#SPJ4

Otras preguntas