Question

The perimeter of a rectangle is 38m. Find the dimensions of the rectangle that will contain the greatest area.

Answer 1

@ganeshie8

Answer 2

@satellite73

Answer 3

anyone?

Answer 4

The area of a rectangle is A = LW

Let the length = x, and the width = y
The perimeter of a rectangle is P = 2x + 2y

In this case, P = 38, so 38 = 2x + 2y, which can be solved for y:
2y = 38 - 2x
y = 19 - x

The area is A = LW.
L = x, and W = 19 - x,
so the area A = x(19 - x)
A = 19x - x^2

Now differentiate with respect to x and set the derivative equal to zero to look for a maximum value:

A' = 19 - 2x
19 - 2x = 0
2x = 19
x = 9.5

y = 19 - 9.5
y = 9.5

This means that L = 9.5 m and W = 9.5 m and the rectangle of greatest area is really a square with side 9.5 m.

Answer 5

hmm. I see. thank you so much @mathstudent55 :)

Answer 6

wlcm