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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.

 Jan 30, 2021
 #1
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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

 

 

cool cool cool

 Jan 30, 2021

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