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
A. The equation s x s = 8100 can be used to determine the side length of the square mat because the given area of the half tatami mat is 8100 cm², and we know that the area of a square is equal to the side length squared. Therefore, by solving for s, we can find the side length of the square mat.
B. We know that the side length of the square mat must be between 50 cm and 100 cm because the given area of the half tatami mat is 8100 cm², which represents half the size of a full mat. Since the full mat is twice the size of the half mat, its area would be 2 x 8100 cm² = 16200 cm².
Now, since the full mat is rectangular, we can take any combination of side lengths that multiply together to give us an area of 16200 cm². For example, the full mat could be 50 cm x 324 cm or 60 cm x 270 cm or 70 cm x 231 cm, and so on.
Since the full mats cover the entire floor except for the half mat, the side length of the square mat must be less than the shortest side length of the full mat. Therefore, the side length of the square mat must be less than 50 cm but greater than 0 cm.
A. We can use the equation s X s = 8100 to determine the side length of the square mat because in a square, all sides are equal in length. In this case, we are given that the area of the half mat is 8100 square cm. Since the area of a square is calculated by multiplying its length and width, we can use the equation to solve for the side length of the square mat.
B. To determine that the side length of the square mat must be between 50 cm and 100 cm, we can use the equation from the previous question, s X s = 8100, and solve for the side length.
If we take the square root of both sides of the equation, we get s = √8100. Simplifying, we find that the square root of 8100 is approximately 90. Therefore, the side length of the square mat is about 90 cm.
Since we are given that the mat is a square half tatami mat, its length and width are equal. So, we can determine the side length by taking the square root of the area.
Since the square root of 8100 is about 90 cm, we know that the side length of the square mat must be less than 100 cm. On the other hand, it must be greater than 0 cm, so we know that the side length must be more than 0. Therefore, it falls within the range of 0 cm to 100 cm.
Additionally, the problem states that the square mat is half the size of a full mat. So, considering that the full rectangular mats cover the remaining floor area, the length and width of the square mat must be less than the length of the rectangular mats, which we can assume to be at least 100 cm. Therefore, the side length of the square mat must be between 0 cm and 100 cm.