Answer:
24 meters is the width of the original rectangle.
Step-by-step explanation:
Given:
Bobby knows that the perimeter of the original rectangle is 120 meters. He also knows that the perimeter of the reduced rectangle is 30 meters and the reduced rectangle has a length of 9 meters.
Now, to get the width of original rectangle.
The reduced rectangle's perimeter = 30 meters.
The reduced rectangle's length = 9 meters.
Now, we find the width of reduced rectangle by using formula:
Let the width of reduced rectangle be [tex]x.[/tex]
[tex]Perimeter=2\times length+2\times width[/tex]
[tex]30=2\times 9+2\times x[/tex]
[tex]30=18+2x[/tex]
Subtracting both sides by 18 we get:
[tex]12=2x[/tex]
Dividing both sides by 2 we get:
[tex]6=x\\\\x=6\ meters.[/tex]
The width of reduced rectangle = 6 meters.
Now, to get the width of original rectangle:
Let the width of original rectangle be [tex]w.[/tex]
As given, the perimeter of the original rectangle = 120 meters.
And, the perimeter of reduced rectangle is 30 meters and its width is 6 meters.
So, 30 is equivalent to 6.
Thus, 120 is equivalent to [tex]w.[/tex]
Now, to get the width using cross multiplication method:
[tex]\frac{30}{6}=\frac{120}{w}[/tex]
By cross multiplying we get:
[tex]30w=720[/tex]
Dividing both sides by 30 we get:
[tex]w=24\ meters.[/tex]
The width of original rectangle = 24 meters.
Therefore, 24 meters is the width of the original rectangle.
