how tall is the tree

Question

Phil, Melissa,​ Noah, and Olivia saw a tall tree that cast a shadow

4242

feet long. They observed at the same time that a

55​-foot-tall

person cast a shadow that was

10.510.5

feet long. How tall is the​ tree?

Answer 1

Let x = height of the tree. Set up two ratios and set them equal, tree lengths in numerator, shadow lengths in denominator.

55/10,510.5 = x/4242

cross multiply

10,510.5x= 55(4242)

x=55/(4242)/10,510.5 = 22.1978 feet

x=about 22.2 feet tall

However, it's hard to read but you seem to have "10.510.5" as one shadow. I'm interpreting that as 10,510.5 Otherwise 2 decimals in a number doesn't make sense.

10,000 is about 2 1/2 times about 4,000, so 55 should be about 2 1/2 times the height of the other tree.

55/(5/2)=22, making 22.2 look about right.