Answer:
5 meters
Step-by-step explanation:
step 1
Find the scale factor
we know that
If two figures are similar, then the ratio of its perimeters is equal to the scale factor
Let
z -----> the scale factor
P1 -----> the perimeter of the reduced rectangle on the right
P2 ----> the perimeter of the original rectangle on the left
[tex]z=\frac{P1}{P2}[/tex]
substitute
[tex]z=\frac{24}{30}=0.8[/tex]
step 2
Find the width of the reduced rectangle on the right
[tex]P1=2(L+W)[/tex]
substitute the given values
we have
[tex]L=8\ m[/tex] ---> see the attached figure to better understand the problem
[tex]24=2(8+W)[/tex]
[tex]12=8+W[/tex]
[tex]W=4\ m[/tex]
step 3
Find the width of the original rectangle on the left
To find the width of the original rectangle on the left, divide the width of the reduced rectangle on the right by the scale factor
so
[tex]W=4/0.8=5\ m[/tex]
