1952 AMC 12 Problem 15

Attempt Problem 15 of the 1952 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 1952 AMC 12 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

15.

The sides of a triangle are in the ratio

6:8:9.

Then:

The triangle is obtuse

The angles are in the ratio

6:8:9

The triangle is acute

The angle opposite the largest side is double the angle opposite the smallest side

None of these

Compare the square of the largest side with the sum of the squares of the other two

Here

9^2

is less than

6^2+8^2

For a triangle with largest side

9,

9^2=81\lt 6^2+8^2=100.

By the converse of the Pythagorean inequality, the angle opposite side

9

is acute. Since it is the largest angle, every angle is acute.

Thus, the correct answer is C.

Problem 15 in other years