Answer:
15000 square feet.
Step-by-step explanation:
From the statement we have that it would be 2 times the length and 3 times the width due to the divisor, therefore, the perimeter would be equal to:
600 = 2 * l + 3 * w
300 = l + 3/2 * w
we solve for w:
l = 300 - 3/2 * w
in addition the area is equal to:
A = w * l
replacing:
A = w * (300 - 3/2 * w)
A = 300 * w - 3/2 * w ^ 2
We derive:
A '= 300 - 6/2 * w
A '= 300 - 3 * w
we equal 0:
300 - 3 * w = 0
w = 300/3
w = 100
replacing and we calculate l:
l = 300 - 3/2 * 100
l = 150
A = 100 * 150
A = 15000 ft ^ 2
The largest area would be 15000 square feet.
