Problem 2 · 2025 Math Kangaroo
Easy
Geometry & Measurement
arearatio
The base of a triangle is extended by 50% and its height is reduced by one third. What is the ratio of the area of the new triangle to the area of the original triangle?
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Answer: B — 1:1
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Hint 1 of 2
A triangle's area is proportional to base times height.
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Hint 2 of 2
Multiply the two change factors together and see what happens to the product.
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Approach: multiply the two scale factors
- Extending the base by 50% makes it \(\tfrac{3}{2}\) of the old base; reducing the height by one third makes it \(\tfrac{2}{3}\) of the old height.
- Area scales by \(\tfrac{3}{2}\times\tfrac{2}{3}=1\), so the area is unchanged.
- The ratio of new area to old is 1:1, answer B.
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