The perimeter of the auditorium screen is 20 meters larger than the perimeter of the library screen.
How to determine how much larger the perimeter of the auditorium screen is
To determine how much larger the perimeter of the auditorium screen is compared to the library screen, calculate the perimeters of both screens and find the difference between them.
Given that the screen in the library has a length of x meters and a width of (x/3) meters, calculate its perimeter using the formula:
Perimeter of the library screen = 2 * (Length + Width)
= 2 * (x + x/3)
= 2 * (4x/3)
= 8x/3
We are given that the library screen has a perimeter of 10 meters, so we can set up the equation:
8x/3 = 10
To solve for x, multiply both sides by 3/8:
x = (10 * 3) / 8
x = 30 / 8
x = 15 / 4
Therefore, the length of the library screen is 15/4 meters.
The length of the auditorium screen is 3 times the length of the library screen, so the length of the auditorium screen is (3 * 15/4) = 45/4 meters.
The width of the auditorium screen is 3 times the width of the library screen, so the width of the auditorium screen is (3 * 5/4) = 15/4 meters.
To calculate the perimeter of the auditorium screen:
Perimeter of the auditorium screen = 2 * (Length + Width)
= 2 * (45/4 + 15/4)
= 2 * (60/4)
= 2 * 15
= 30
Therefore, the perimeter of the auditorium screen is 30 meters.
To find how much larger the perimeter of the auditorium screen is compared to the library screen, subtract the library screen's perimeter from the auditorium screen's perimeter:
Perimeter difference = Perimeter of auditorium screen - Perimeter of library screen
= 30 - 10
= 20
Hence, the perimeter of the auditorium screen is 20 meters larger than the perimeter of the library screen.
The screen in the auditorium is 3 times as long as the screen in the library and a width 3 times as much the screen in the library is 3 meters long with a perimeter of 10
How much larger is the perimeter of the auditorium screen?