Question

If the line 3x + 4y = p makes a triangle
of area 24 square unit with the co-ordinate
axes then find the value of p.​

Answer 1

Formula:

If A (x₁, y₁), B (x₂, y₂), C (x₃, y₃) be the vertices of a triangle, then the area of triangle ABC is

= 1/2 * {x₁ (y₂ - y₃) + x₂ (y₃ - y₁) + x₃ (y₁ - y₂)} square units

For the same triangle, the mid-points of the sides are given by

( (x₁ + x₂)/2 , (y₁ + y₂)/2 )

( (x₂ + x₃)/2 , (y₂ + y₃)/2 )

( (x₃ + x₁)/2 , (y₃ + y₁)/2 )

Solution:

The given straight line is

3x + 4y = p

or, x/(p/3) + y/(p/4) = 1

So the line intersects the coordinate axes at (p/3, 0) and (0, p/4)

Given that, the points (0, 0), (p/3, 0) and (0, p/4) forms a triangle whose area is 24 square units

Then 1/2 * [0 (0 - p/4) - 0 (p/3 - 0) + 1 (p²/12 - 0)] = 24

or, p²/12 = 2 * 24

or, p² = 48/12

or, p² = 4

or, p = ± 2

∴ the value of p is ± 2

Answer 2

Answer:

Step-by-step explanation: