Challenge Problem Archive - 5/6/02 - Take it to the Max

[Bills_E]

Given that ABCD is a rectangle, is the area of triangle ABE > 25 ?

(Note: Figure above is not drawn to scale).

(1) AB = 6

(2) AE = 10

The answer is based on the fact that the right triangle with the largest area will be an isosceles right triangle.

AB is the base of the triangle and therefore will have an area of 1/2*6*6 = 18. Enough to answer the question.

But the answer to the problem is "B". What am I missing?

PS: I have not yet figured out how to post the image... [/url]

[Anadi]

The rule that isoceles right angle triangle has the maximum area applies when the hypotnuse is the fixed length, which is AE here.

If just AB is fixed, triangle can have other side of any length and the corresponding hypotnuse, and area will keep increasing till you cover half the rectangle and in our case, we do not have rectangle's dimensions. So 1 is not sufficient.

[JadranLee]

That's right, Anadi. Here's the link for the full problem online, in case people want to look at the diagram and the original explanation: http://www.manhattangmat.com/ChallengeP ... ChallID=17

-Jad