math question please help!?

Question

an 8.5 x 11 inch sheet of paper is cut in half lengthwise, while an identical sheet of paper is torn in half widthwise. do the resulting half sheets have the same area, perimeter, or both?

Answer 1

First way, 8.5 x 11 becomes 4.25 x 11
area = 4.25 * 11
=46.75in^2

perimeter = 2(4.25+11)
=30.5in


Second way, 8.5 x 11 becomes 8.5 x 5.5

area = 8.5 * 5.5
=46.75in^2

perimeter = 2(8.5+5.5)
=28in

The resulting sheets have the same area, 46.75in^2

Answer 2

Each half-sheet has half of the area of the original paper, so the areas are the same.

When you make the lengthwise cut, you've added twice the length to the combined perimeters, and each of the identical halves have half the combined perimeter; when you make the widthwise cut you've added only twice the width etc. so the perimeters are different.

On the other hand, if you make widthwise cuts in two distinct places on two sheets of paper (like halfway on one, and 1/3 of the way from the nearer edge on the other) those four half-sheets would have different areas (except the two from the paper cut exactly in half) but the combined perimeters of one pair would be the same as the combined perimeters of the other pair.

Answer 3

@ lenghtwise area = 4.25 x 11 = 46.75 sq in
@ widthwise area = 5.5 x 8.5= 46.75 sq in
for perimeter @ 4.25 x 2 + 11x2 = 8.5+22= 30.5 in
@5.5x2 + 8.5x2 = 11 + 17 = 28 in
therefore areas are equal but the perimeters are not the same.

Answer 4

the first way: you get a piece of paper 4.25 x 11
area = 46.75 perimeter: 30.5

the second way: you get a piece of paper 8.5 x 5.5
area: 46.75 perimeter: 28

Answer 5

same area, but diff perimeter.

area=46.75
p1=11*2+4.25*2=30.5
p2=5.5*2+8.5*2=28

Answer 6

my suggestion would be to actually try it and find out, you may be surprised.

Answer 7

Why not just try it?

Answer 8

yea they should be identical