Problem
Peter measures the heights of two trees and the lengths of their shadows. He notices that the height of each tree and the length of its shadow are directly proportional. One of the trees has a height of $12 \mathrm{~m}$ and an $8 \mathrm{~m}$ long shadow. The other tree has a $13.8 \mathrm{~m}$ long shadow. Calculate its height, in metres $(\mathrm{m})$. Give any decimal answers to 1 d.p.
Solution
Step 1 ：Let the height of the second tree be x. We can set up a proportion:
Step 2 ：\(\frac{12}{8} = \frac{x}{13.8}\)
Step 3 ：Now we can solve for x:
Step 4 ：\(x = \frac{12 \times 13.8}{8}\)
Step 5 ：\(x = 20.7\)
Step 6 ：\(\boxed{20.7}\)
