A kindergarten school has square mats in two colors, red and blue. The ratio of the perimeter of the red mat to the perimeter of the blue mat is 2 : 1. The area of the blue mat is 36 square feet.
What is the area of the red mat?
whats a ratino
and then ill help because i have no idea what that means
plus wouldnt the answer be 36 because there both square and there distance isnt far
if linear dimensions are scaled by n, area is scaled by n^2
Since red:blue perimeter is 2:1,
red:blue area is 2^2:1
4*36 = 144
144
To find the area of the red mat, we need to first find the length of the sides of both mats.
Let's denote the side length of the red mat as 'r' and the side length of the blue mat as 'b'.
Since the ratio of the perimeter of the red mat to the perimeter of the blue mat is 2:1, we can set up the following equation:
2r / (4b) = 2 / 1
The ratio of the perimeter (2r for the red mat and 4b for the blue mat) is equal to the given ratio (2:1). We divide each side by 4b since the blue mat has four sides.
Cross-multiplying the equation, we get:
2r = 2(4b)
2r = 8b
Next, we need to find the value of 'b'. We know that the area of the blue mat is 36 square feet.
The area of a square is calculated by multiplying the length of its sides, so we have:
b^2 = 36
Taking the square root of both sides, we find that b = 6.
Substituting this value of 'b' back into the equation 2r = 8b:
2r = 8(6)
2r = 48
Dividing by 2, we find that r = 24.
Therefore, the side length of the red mat is 24 feet. To find the area of the red mat, we calculate:
Area of the red mat = r^2 = 24^2 = 576 square feet.
So, the area of the red mat is 576 square feet.