1952 AMC 12 Problem 38
Attempt Problem 38 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).
38.
The area of a trapezoidal field is square yards. Its altitude is yards. Find the two bases, if the number of yards in each base is an integer divisible by The number of solutions to this problem is:
None
One
Two
Three
More than three
Answer: D
Small hint:
Use the trapezoid area formula to find the sum of the two bases
Big hint:
List the unordered pairs of positive multiples of with that sum
Solution:
If the bases are then so The unordered positive pairs of multiples of are There are three solutions.
Thus, the correct answer is D.