Question

A rectangular pen is made with 100 m of fencing in three sides. The fourth is a stone wall. Find the greatest possible area of such an enclosure.

Answer 1

please help me

Answer 2

\[ 1250 \ m^2\]

Answer 3

So first multiply the x through to get 100x - 2x^2. Then its derivative would be 100 - 4x. Setting that equal to zero and solving for x gives us x = 25. So the 100 - 2x side equals 50. Thus our max area = 25 X 50 = 1250m^2.

Answer 4

can you write it step by step? im sorry i just so confused

Answer 5

a(x,y)=xy

x + 2y = 100, x = 100 - 2y

a(x,y) = xy

Substitute
a(y) = (100 - 2y)y, a(y) = 100y-2y^2

a'(y) = 100-4y

Solve for y when a'(y) = 0

0 = 100 - 4y, y = 25

Recall
x + 2y = 100

x + 2(25) = 100, x = 50

(x,y) = (50, 25)