A rectangle has a perimeter of 32 in. Find the length and width of the rectangle under which the area is the largest. a. Let the width to be x and the length to be y , then the quantity to be maximized is (expressed as a function of both x and y) A=
b. The condition that x and y must satisfy is y=

Length of the rectangle is 8 in and the breadth is 8 in.

a.

b.

Step-by-step explanation:

Length = x

Breadth = y

Area is given by

Perimeter of rectangle is given by

The condition that x and must satisfy is

So, area is

Differentiating with respect to x we get

Equating with zero

Double derivative of A(x)

So which means is maximum at

So length of the rectangle is 8 in and the breadth is 8 in.

-1, -2, -3, -4, -6

step-by-step explanation:

mk./km: lm

step-by-step explanation:

,mlmlm

; mk

lk