1979 AHSME Problems/Problem 30
In , is the midpoint of side and is on side . If the length of is and and , then the area of plus twice the area of equals
Let be the point on the extension of side past for which . Since and , is equilateral. Let be the point on line segment for which . Then is similar to and . Also is congruent to . Therefore, . Plugging in the values that we know and then dividing by 2 results in an answer of
This solution is from the solution manual but was typed here by alpha_2.