Find the length and width of a rectangle that has the given

Find the length and width of a rectangle that has the given perimeter and a maximum area.

Perimeter: 116 meters

Solution

Permiere = 1167 mt

lenght =l

width = w

2l +2w = 116

l +w = 58

Area = l*w = l( 58-l) = -l^2 +58l

maximum area occurs at l = -b/2a for a quadratic function -2l +58

l = -(58)/(2*-1) = 29 mt

w= 116/29 = 4 mt

Soluition : length = 4 mt

wifth = 29 mt

Maximum area a =