Question

The question is:

A gardener wishes to create a rectangular bed. There are 70 meters of fencing wire which will be used to fence three sides of the garden bed, with a brick wall forming the fourth side. Calculate the maximum area of the garden bed that can be created, and state it's dimensions.

Guys can you see where I went wrong.

I worked out this question by starting to work out the perimeter of the three sides.
P = 2x + y
70 = 2x + 7
y = 70 - 2x

Then I used it in the area equation:
A = lw
A = (70 - 2x)(x)

I got a max area of 612.5 m^2, which is correct.
And I got x = 0, x = 35. When I substitute 35 or 0 into the initial equations(70-2x) or (x). I get one of them as 0. Please help!

Answer 1

as you say, y = 70-2x, and the area

a = xy = x(70-2x)
You found the roots of that function <u>which is where the area is zero</u>!

The vertex of a parabola is midway between the roots, at x = 17.5
So, y=35 and the maximum area is indeed 612.5

Answer 2

Thanks for your answer! I released that I posted this twice on accident.