The length and width of a rectangular projector screen in a small theatre is 200% more than the length and width of a television screen in the same room. How much bigger is the area of the screen than that of the television? Give your answer as a percentage.
200% more means three times as large
the length and width of the projector screen are three times the length and width of the television screen
this means the area of the larger screen is nine times the area of the smaller
nine times means 800% more
To find out how much bigger the area of the projector screen is compared to the television screen, we first need to know the dimensions of the television screen.
Let's assume the length of the television screen is 'L' and the width is 'W'.
According to the given information, the length and width of the projector screen are 200% more than the length and width of the television screen.
To calculate the length and width of the projector screen, we can multiply the length and width of the television screen by 200% (or 2).
The length of the projector screen would be 2L, and the width would be 2W.
Now, let's calculate the area of both screens.
The area of the television screen is given by A_television = L * W.
The area of the projector screen is given by A_projector = 2L * 2W = 4LW.
To find out how much bigger the area of the projector screen is, we can calculate the percentage increase.
The percentage increase in area is given by:
Percentage increase = (A_projector - A_television) / A_television * 100.
Substituting the values we have:
Percentage increase = (4LW - LW) / LW * 100 = 3LW / LW * 100 = 300%.
Therefore, the area of the projector screen is 300% bigger than the area of the television screen.