Call the point where the dashed line intersects FG point K. Given: .. FK = x+6 .. FG = HI = 3x .. FI = x+8 = GH = 2x -1 .. Area of a parallelogram = HI*IK .. Pythagorean theorm says FK^2 +IK^2 = FI^2
Find: .. x .. Area
Solution: .. Using the fact that FI = GH, we find .. x +8 = 2x -1 .. 9 = x . . . . . . . . . add 1-x to both sides of the equation
Now, we know .. FK = 9 +6 = 15 .. HI = 3*9 = 27 .. FI = 9 +8 = 17 .. FK^2 +IK^2 = FI^2 .. 15^2 +IK^2 = 17^2 .. Ik^2 = 289 -225 = 64 .. IK = √64 = 8
