I want to use 376 ft of fencing to fence off the greatest possible rectangular area what would be my dimensions to use for the garden

If you know what the perimeter has to be, and you want it to

enclose the greatest possible area, then you make it a circle.

If it has to be a rectangle, then you make it a square.

Since you have 376-ft of fence, the sides of the square

should be (1/4 of 376) = 94 feet.

The enclosed area is (94²) = 8,836 ft².

I can't prove to you that this is the greatest possible area

(without some calculus), but I can demonstrate it:

Let's distort the square slightly. Take, say, 1 foot off the length,

and make it 1 foot wider. The perimeter doesn't change, but

the area becomes

(93) x (95) = 8,835 ft².

As soon as we re-shaped the garden away from square, the

area began to drop.

The less square we make it ... even while keeping the same perimeter ...

the smaller the area becomes. Here are 4 more gardens, all with perimeters

of 376-ft:

(84) x (104) = 8,736 ft²

(74) x (114) = 8,436 ft²

(64) x (124) = 7,936 ft²

(54) x (134) = 7,236 ft²

The only way to get more area out of the same length of fence is to

make the garden a circle.

Circumference = 376 ft

Radius = (circumference) / 2π = 188/π

Area = πR² = π (188/π) ² = 11,250.3 ft²

That's about 27% more area than the square.