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At the same moment, a 2 m pole and a tree cast the shadows shown (lengths drawn to scale). Heights and shadows are in proportion. How tall is the tree?

Class 6Ratio and ProportionRatio and Proportion
  • A10 m
  • B22.5 m
  • C14 m
  • D7.5 m

Step-by-Step Solution

Height : shadow is the same for both: . Since , height m. (22.5 m flips the ratio; 14 m adds 12 instead of multiplying.)
Answer: A) 10 m

Key idea: What a ratio means

The ratio 2 : 3 says: for every 2 of one thing, there are 3 of another. In a fruit basket of 2 apples and 3 oranges, the ratio of apples to oranges is 2 : 3. **Order matters** — the ratio of oranges to apples in the same basket is 3 : 2. The two quantities must be in the same unit (you can't ratio apples to kilograms unless you convert).

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