Question

The ceiling of Katie’s living room is a square that is 20 ft long on each side. To decorate for a party, she plans to hang crepe paper around the perimeter of the ceiling and then from each corner to the opposite corner. Katie can buy rolls that each contain 25 ft of crepe paper.

What is the minimum number of rolls she should buy?

Draw a diagram, show your work and explain your reasoning.

Answer 1

Explanation:

To calculate the total length of crepe paper Katie needs to buy, we first need to find the length of each diagonal of the ceiling.

Since the ceiling is a square, the length of each diagonal can be found using the Pythagorean theorem:

diagonal^2 = side^2 + side^2

diagonal^2 = 2 * side^2

diagonal = sqrt(2 * side^2)

diagonal = sqrt(2 * 20^2) = sqrt(800) = 20 * sqrt(2)

So the length of each diagonal is 20 * sqrt(2) ft.

Katie needs to hang crepe paper around the perimeter of the ceiling, which is 4 * 20 = 80 ft long.

She also needs to hang crepe paper from each corner to the opposite corner, which means she needs to cover the length of each diagonal twice. So the total length of crepe paper she needs is:

2 * 20 * sqrt(2) + 80 = 40 * sqrt(2) + 80 ≈ 131.31 ft

Therefore, Katie needs to buy at least 6 rolls of crepe paper (since each roll contains 25 ft of crepe paper).