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 ABC,ABC, AB=12,AB=12, AC=7,AC=7, and BC=10.BC=10. If sides ABAB and ACAC are doubled while BCBC 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 00

Answer: E
Concepts:triangle inequalityarea
Difficulty rating: 1450
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 24,24, 14,14, and 10.10. Because 14+10=24, 14+10=24, they form a degenerate triangle: all three vertices are collinear. Its area is therefore 0.0.

Thus, the correct answer is E.

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Problem 46 in Other Years

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