Answer:
27 foot or 324 inches
Step-by-step explanation:
Given: A 6 foot tall football player casts a 16 inch shadow. At the same time the stadium bleachers cast a 6 foot shadow.
To find: how tall are the bleachers
Solution:
It is given that a 6 foot tall football player casts a 16 inch shadow.
So, the height of the footballer in inches is \(12\times6=72\) inches.
we have the ratio of the height of football player to the shadow is \(\frac{72}{16}\)
Length of shadow in inches is \(12\times6=72\) inches.
Now, let the height of the bleachers be h.
So, the ratio of bleachers height to the shadow is \(\frac{h}{72}\)
Since, at the same time the stadium bleachers cast a 6 foot shadow. So, the ratio of height of bleachers to the shadow is same as the ratio of the height of football player to the shadow.
On solving,
\(\frac{h}{72} =\frac{72}{16}\)
\(\implies h=\frac{72\times72}{16}\)
\(\implies h=36\times9\)
\(\implies h=324\) inches or \(\frac{324}{12}=27\) foot
Hence, the height of bleachers is 324 inches or 27 foot.
