Problem Solving

Is there a simpler solution

Waiting for a solution

I can only speak for myself, but I would imagine no one responded because no one knows how to interpret the point (?7, ?3).

I'll assume that ? means - and try to explain the question accordingly. (I thought it meant √ at first, but I wasted 5 minutes trying to solve it that way and getting a hideous answer.)

The distance from (-2, 9) to (-7, -3), using the distance formula, is √((-3-9)² + (-7 - (-2))²), or √(144 + 25), or 13.

The ratio of height to side is an equilateral triangle is x√3 :: 2x. (To see why, draw the height and notice that you've created two 30-60-90 triangles. So half the base is x, the height is x√3, and the side of the equilateral is 2x.)

So the sides are 13 * 2/√3.

Area is (bh/2), so (13 * 2/√3 * 13)/2, or 169/√3, or (169*√3)/3.

Thanks for the solution Matt, and sorry I missed the typo!!