Question

A triangle is formed by the x axis and the lines 2x+y = 4 and x-y = 0 as three sides. Taking the side along x axis as its base the corresponding altitude of the triangle is

Answer 1

First find the vertices which is not lying on the X exes and then find its y value by solving both the equations Simultaneously. Answer is 4/3.

Answer 2

1 – y + 1 = 0

⇒ y = 2

∴ The intersection of the equations is (1,2)

Now, we have to find out the intersection of 2x + y = 4 with x and y axis

Putting x = 0 in this equation, we get

y = 4

Putting y = 0 in this equation, we get

2x = 4

⇒ x = 2

∴ Intersection of this equation with x and y axis are (2,0) and (0,4)

Now, we have to find out the intersection of x – y + 1 = 0 with x and y axis

Putting x = 0 in this equation, we get

. y = 1

Putting y = 0 in this equation, we get

X = - 1

∴ Intersection of this equation with x and y axis are (-1,0) and (0,1)

From graph, Taking the side along x-axis as its base, the corresponding altitude of the triangle = AB

= 2 units