AleksandrM wrote:I've only been able to arrive at the height of the triangle, which is 13.
This triangle will obviously have angles 60:60:60, and all three sides will be equal... hence, equilateral.
You can split the triangle into two right angle triangles with base 13, but we will then need one of the other two heights. The triangle will be 90:60:30 with sides x:xroot3:2x.
Hope someone can take this further.
You're almost there!
The height of an equliateral triangle is the xroot3 side of the 30/60/90 triangle.
To calcuate the area of the triangle, we also need the base - so, we need to solve for x.
xroot3 = 13
x = 13/root3
The base of the equilateral triangle is actually the 2x side (since every side is the same), so the base is 2*(13/root3) or 26/root3
Area = 1/2 * base * height
Area = 1/2 (26/root3) (13)
Area = 169/root3
If that appears among the answers, we're done. However, most GMAT answer choices "rationalize the denominator", which basically means getting rid of the root. To do so, we multiply the top and bottom of the fraction by the root itself.
169/root3 = 169(root3)/root3(root3) = 169root3/3
In all likelihood, that's the actual correct answer.
