Answer:
length of the sheet of paper is 11 in.
Step-by-step explanation:
Let "a" = short end of paper and let "b" = long end of paper.
Let "p" = perimeter
1st equation: p = 39"
2nd equation: 2a + 2b = p plug in "39" for diameter; result:
2nd equation: 2a + 2b = 39
3rd equation: b = 2a - 6
replace "b" in 2nd equation with "2a - 6" from 3rd equation, result:
2a + 2(2a - 6) = 39 simplified to:
2a + 4a - 12 = 39 simplified to:
6a - 12 = 39 simplified to:
6a = 51 simplified to:
a = 51/6 = 8.5
so, a = short end of paper = 8.5 inches
In 3rd equation (b = 2a - 6), substitute "a" with "8.5"
3rd equation becomes: b = 2(8.5) - 6 simplified to:
b = 17 - 6 = 11
so, b = long end of paper = 11 inches
answer to question is: dimensions of paper are ---
8.5 inches wide by 11 inches long
