Answer:
The perimeter of the auditorium is 30 meters
Step-by-step explanation:
The question is
What is the perimeter of the screen in the auditorium?
we know that
If two figures are similar, then the ratio of its perimeters is equal to the scale factor
In this problem, the auditorium and the library are similar
Let
z ----> the scale factor
x ----> the perimeter of the auditorium
y ----> the perimeter of the library
so
[tex]z=\frac{x}{y}[/tex]
we have
[tex]z=3[/tex] ----> the scale factor is given
[tex]y=10\ m[/tex]
substitute
[tex]3=\frac{x}{10}[/tex]
solve for x
[tex]x=3(10)=30\ m[/tex]
therefore
The perimeter of the auditorium is 30 meters
For educational purposes
Find the width of the library
we know that
[tex]P=10\ m\\P=2(3+W)[/tex]
so
[tex]10=2(3+W)\\5=W+3\\W=2\ m[/tex]
Find the dimensions of the auditorium
To find out the dimensions of the auditorium multiply by 3 (the scale factor) the dimensions of the library
so
[tex]L=3(3)=9\ m\\W=3(2)=6\ m[/tex]
Verify the perimeter
[tex]P=2(9+6)=30\ m[/tex] ----> is correct
