Question

Suppose you have a 7-cm by 5-cm rectangle. You increase the length by 1 cm and decrease the width by 1 cm. You continue to do this. What happens to the perimeter of the rectangle? The area? Explain why this happens.

Answer 1

Answer:

Step-by-step explanation:

P of original = 14 + 10 = 24

P of original l + 1  and w - 1 = 16 + 8 = 24

P of original l + 2  and w - 2 = 18 + 6 = 24

The perimeter remains the same each time since Perimeter is to the 1st power and you are summing; by subtracting from one and adding the same amount to another measure there is no change in perimeter

A of original = 7 x 5 = 35

A of original l + 1  and w - 1 = 8 x 4 = 32

A of original l + 2  and w - 2 = 9 x 3 = 27

A of original l + 3  and w - 3 = 10 x 2 = 20

A of original l + 4  and w - 4 = 11 x 1 = 11

The area decreases by 3,5,7,9 units each time since Area is to the 2nd power since you are multiplying two measures, now if you take the 2nd differences of 3,5,7,9 you see that they are 2 units apart each time, so are is squared and the 2nd differences are constant