Math
posted by Bella S on .
Vanessa presented a report on Japanese tea rooms to her class. The floors are usually covered with square and rectangular tatami mats. She drew one way to cover square floor with a square half tatami mat qnd four rectangular full mats. The area if the half mat is 8100cm (square) and is half the size of full mat.
A. The variable s presents the side length of square mat. Why can you use the equation s X s=8100 to to determine the aide length of th square mat?
B. How do yy know that the aide length of the square mat must be between 50 cm and 100 cm?

area = length * width
for the square mat s is the length and the width
so
Area of square mat = s*s = s^2 = 8100 cm^2
so s = sqrt(8100) = 90 cm
The area of each of the big rectangular mats is twice the square one , therefore 2*8100 = 16,200 cm^2 and it is 90cm by 180 cm
Lay a square room out with the square mat in upper left, one rectangle sticking out from it right
then three rectangles below those two sticking down
This gives you a square room, 3s * 3 s or 270cm * 270 cm = 72,900 cm^2
50^2 = 2,500 too small
100^2 = 10,000 too big
right answer is 90^2 = 8,100