Question

Justin wants to use 188 ft of fencing to fence off the greatest possible rectangular area for a garden. What dimensions should he use? What will be the area of the garden?

Answer 1

A. 89 x 99 ; 8811 ft

B. 92 x 96 ; 8832 ft

C. 94 x 94 ; 8836 ft

D. 93 x 95 ; 8835 ft

Answer 2

Well if they give you the options then you can just see which ever number is the highest, which would be C. 94 by 94.

Answer 3

I'm guessing you want to know how you would solve it without the options laid out for you?

Answer 4

yes please, this confuses me.. @Hitaro9

Answer 5

Okay. First we should try setting up an equation for the area.

Answer 6

letting A = Area

A is going to be X (the side of one fence) times (188-X) cause you're going to use the remaining fence to construct the other side.

Answer 7

So A = x(188-x)
or A = 188-x^2

Answer 8

You should be able to recognize that that's a parabola equation, an upside down one at that cause the x^2 is negative.
A= -x^2+1888

Answer 9

So you know it's going to have a maximum

Answer 10

And the x value will be the side of one fence, and the other side will be 188-x (which we defined earlier.

Answer 11

Thank you so much for explaining! That really helped :) @Hitaro9

Answer 12

No problem.

Answer 13

Oh yeah, small correction, should have been

-x^2+188x

My bad.