GMAT Question of the Day - Problem Solving - Geometry/Puzzle
The measurements obtained for the sides of a certain triangle are 18 centimeters by 18 centimeters by 18 centimeters. If each of the sides has a measurement error of at most 2 centimeters, which of the following is equal to the maximum possible difference between the actual area of the triangle and the area calculated using these measurements?
GMAT Question of the Day Solution
Although this GMAT question involves geometry it is also a bit of a puzzle because of the measurement error portion. If you're not sure how the measurement error will affect the area you might want to try some small numbers to get a feel for the question. Try a triangle with sides measuring one versus a triangle with sides measuring three. Let's remember that we want the maximum difference so you should make the measurement error a plus not a minus. Why a plus? Because the bigger the numbers the more the difference of two will make. The difference between 1000*1000 and 1002*10002 is much greater than the difference between 3*3 and 5*5. So we want the numbers to be as big as possible.
The other thing that will help in this question of the day is: the formula for the area of an equilateral triangle. For my GMAT tutoring students I try to keep the esoteric formulas to a minimum (no memorizing standard deviation here!) but this formula is useful. Side^2 * (√3/4)
Once you set up the expression you should notice that you can factor out √3/4. Once you've done that you'll see a difference of squares. Go for it! Using this special quadratic will make the simplifying easier.