Question

Please Help Soon! A 4-foot by 8-foot rectangular piece of plywood will be cut into 4 congruent rectangles with no wood left over and no wood lost due to the cuts. What is the positive difference, in feet, between the greatest possible perimeter of a single piece and the least possible perimeter of a single piece?

Answer 1

Answer: 6 feet

Step-by-step explanation:

Given that a 4-foot by 8-foot rectangular piece of plywood will be cut into 4 congruent rectangles with no wood left over and no wood lost due to the cuts

Let assume that the 4 rectangles will be of the same area since they are congruent.

The area of the big rectangle will be

Area = 4 × 8 = 32

Divide 32 by 4

32/4 = 8

Suggest the two possible numbers in which their product will be equal to 8

4 and 2 or 8 and 1

If 4 and 2

The perimeter = 2L + 2B

Substitute the 4 and 2 into the formula

Perimeter = 2(4) + 2(2)

Perimeter = 8 + 4

Perimeter = 12

If 8 and 1

Perimeter = 2(8) + 2(1)

Perimeter = 16 + 2 = 18

The positive difference, in feet, between the greatest possible perimeter of a single piece and the least possible perimeter of a single piece will be:

18 - 12 = 6 feet