Question

find the ratio of areas of 2 triangles formed by the lines 3x+y-12=0,x-3y=-6 one with x axis and one with y axis

Answer 1

1:1 the area of both the triangles will be (1/2)*(10)*(3)=15 square unts
Hint: draw the figure and mark the coordinates of triangles formed and find their areas.
thanks

Answer 2

Given : 2 triangles formed by the lines 3x +y-12=0,x-3y=-6 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

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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