Find the ratio of areas of 2 triangles formed by the lines 3x + y - 12 =0 , x - 3y + 6 = 0 one with x-axis and one with y-axis .
Answers
Given : 2 triangles formed by the lines 3x +y-12=0,x-3y + 6=0 one with x axis and one with y axis
To Fins : ratio of areas of 2 triangles
Solution:
3x +y-12=0,
x-3y + 6 = 0
on solving x = 3 , y = 3
Distance of point from both axis is 3
other two points with x axis => y = 0
( 4 , 0) and ( -6 , 0)
Hence Base = 4 - (-6) = 10
other two points with y axis => x = 0
(0 , 12) and (0 , 2)
Hence Base = 12 - 2 = 10
Base and height of both triangle are same
Area of each triangle = (1/2) * base * height
= (1/2) * 10 * 3 = 15 sq units
ratio of areas of 2 triangles is 1: 1
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