Two triangles have equal area x, find x
Source: BAMO 2023/3
March 3, 2023
geometry
Problem Statement
In the following figure—not drawn to scale!— is the midpoint of , triangle has area , and quadrilateral has area . Triangles and have the same area, . Find .
[asy]
unitsize(2cm);
pair A = (0,38/16);
pair B = (0,0);
pair C = (38/16,0);
pair D = (0,25/16);
pair E = (19/16,0);
pair F = .4*D+.6*C;
draw(D -- C -- B -- A -- E -- F);
label("", A, W);
label("", B, W);
label("", C, S);
label("", D, W);
label("", E, S);
label("", F, N);
label("", (17*F-8*C)/9, NE);
[/asy]