dimension word problems

Question

2400 feet of fencing will be used to enclose a rectangular corral split into 7 pens of equal size. find the dimensions of the corral that will enclose the greatest possible area

Answer 1

In order to enclose the greatest area you want the overall rectangle to be a square.

Draw a square with side length x

Inside this square put 6 parallel lines, either horizontal or vertical...

Each of those lines will also be length x.

 

Thus we end up with 10 lines of length x.

These sum to 2400 ft

 

10x = 2400

x = 240 ft

 

The area enclosed overall is x²

240² = 57,600 ft² of enclosed corral.