Question

a kennel owner has 270 feet of fencing material to be used to divide a rectangular are into 10 equal pens. Find the dimensions that would allow 100ft2 for each pen

Answer 1

The dimensions for each pen would be 27 feet by 3.7 feet.

Step-by-step explanation:

To find the dimensions of each pen, we need to divide the total fencing material by the number of pens to get the length of each side. Since there are 10 pens and 270 feet of fencing material, each pen will have 270/10 = 27 feet. Since we want an area of 100ft2 for each pen, we can calculate the width as follows:

Area of a rectangle = length x width
100 = 27 x width
width = 100/27 = 3.7 feet

Therefore, the dimensions for each pen would be 27 feet by 3.7 feet.

Answer 2

Because the fencing material will be placed after the first pen and before the 10th pen, the fencing material that the kennel owner have will have to be divided only by 9. This give us an answer of 30 ft.

The calculated 30 ft above is equal to the width of the pen. The width is calculated by dividing the area by the length. This gives us,
width = 100 ft² / 30 ft
width = 3.33 ft
The dimension of the rectangle is therefore, 33.3 ft width and the length of 30 ft.