A 40-foot by 10-foot rectangular garden is enclosed by a fence. To make the garden larger, while using the same amount of fencing, its shape is changed to a square. How many square feet larger than the old garden is the new garden?

Step-by-step explanation:

This 40-foot by 10-foot garden would have an area of 400 feet ...

40 x 10 = 400

It would also use a total of 100 feet of fencing ...

40 + 10 + 40 + 10 = 100

To find how long each side would be if it were transformed into a square, simply divide 100 by 4 ...

100 / 4 = 25

Now that each side is 25 feet, we need to figure out what the area of the new garden is, and how much larger it is than the old garden ...

25 x 25 = 625

This is the area of the new garden.

Area of the old garden = 400 square feet

Area of the new garden = 625 square feet

The new garden is 225 square feet larger than the old garden!

225 square feet

Step-by-step explanation:

Area of the rectangular garden

The area of the rectangular garden is:

40 * 10 = 400 square feet

Size of the new square garden

First we find the perimeter of the old garden:

(40 x 2) + (10 x 2) = 100 feet of fencing

Then we find the size of the new garden, because it is a square we divide by 4:

100 : 4 = 25 feet

Area of the new garden

The area of the new garden is:

25 x 25 = 625 square feet

The difference is 625 - 400 = 225 square feet