1950 AMC 12 Problem 46
Attempt Problem 46 of the 1950 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1950 AMC 12 solutions, or check the answer key.
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46.
In triangle and If sides and are doubled while remains the same, then:
The area is doubled
The altitude is doubled
The area is four times the original area
The median is unchanged
The area of the triangle is
Answer: E
Small hint:
Write down the three new side lengths
Big hint:
Compare the largest new side with the sum of the other two
Solution:
The new side lengths are and Because they form a degenerate triangle: all three vertices are collinear. Its area is therefore
Thus, the correct answer is E.