The approximate dimensions of the playing surface are 45m in length and 5m in width.
The area of a rectangular sheet of ice for curling is about 225m². The width is about 40m less than the length. To find the approximate dimensions of the playing surface, we can set up the following equation:
Let's denote the length of the rectangular sheet as L and the width as W. We are given that the area (A) is 225m², and the width is 40m less than the length, so we have:
A = L * W
225 = L * (L - 40)
Now, we can solve for the length (L) by factoring the equation:
L² - 40L - 225 = 0
Using the quadratic formula, we get:
L = (40 ± √(40² - 41(-225))) / (2*1)
L = (40 ± √(1600 + 900)) / 2
L = (40 ± √2500) / 2
L = (40 ± 50) / 2
The solutions for L are:
L = (40 + 50) / 2 = 90 / 2 = 45
L = (40 - 50) / 2 = -10 / 2 = -5
Since the length cannot be negative, the length of the rectangular sheet is 45m. Now, we can find the width (W) by subtracting 40 from the length:
W = L - 40
W = 45 - 40
W = 5
Therefore, the approximate dimensions of the playing surface are 45m in length and 5m in width.
Complete question:
The playing surface in the game of curling is a rectangular sheet of ice with an area of about 225m^2. The width is about 40 m less than the length. How do you find the approximate dimensions of the playing surface?