Question

find the area of the triangle formed by the lines 2 X + Y= 6 and 2 x - y + 2 =0 with the x axis. *​

Answer 1

1)2x+y=6

⟹y=6−2x

Let, x=1, then y=6−2(1)=4

Similarly, when x=2,y=2

x−2y+2=0

⟹x=2y−2

Let, y=0, then x=2(0)−2=−2

Similarly, when y=2,x=2

Plotting the above points on the graph, we get, the vertices of the traingle, i.e. A(2,3),B(3,0),C(−2,0)

∴ Area of the triangle =

2

1

×5units×2units

=5 sq. units

2)According to the question, the graph of the line would be;

On solving, we get point as (1,4).

ar(△DOC)=

2

1

(OD)(OC)=

2

1

×1×2=1sq.units

ar(△AOB)=

2

1

(OB)(OA)=

2

1

×3×6=9sq.units

∴ Ratio of areas = 1:9