In a rectangle ABCD, AB=5cm,BC=3cm. Points F and G lies on line segment CD such that DF=1cm,GC=2cm. Lines AF and BG when joined and extended intersects at E. Find the area of triangle ABE.
+128475 Not too difficult
Let A = (0,0) B = (5,0) C =( 5,3) D =(0,3) F = (1,3) G = (3,3)
The slope of the line containing AF is 3
And the equation of the line containing AF is y =3x
The slope of the line containing BG is ( 3-0) / ( 3-5) = -3/2
And the equation of the line containing BG is y =(-3/2)( x -5) = -3/2x + 15/2
The x intersection of these lines is
3x = -(3/2)x + 15/2
9/2x = 15/2
9x =15
x = 15/9 = 5/3 = x coordinate of E
And the y coordinate of E is y = 3(5/3) = 5 = the altitude of ABE
Area of ABE = (1/2) AB * altitude = (1/2)(5)(5) = 25/2 = 12.5
