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

Let the line 3x + 4y = p cuts the X and Y axes at points A and B respectively.

3x + 4y = p

∴ `(3"x")/"p" + (4"y")/"p"` = 1

∴ `"x"/("p"/3) + "y"/("p"/4)` = 1

This equation is of the form `"x"/"a" + "y"/"b"` = 1,

where a = `"p"/3` and b = `"p"/4`

∴ A ≡ (a, 0) = `("p"/3, 0)` and B ≡ (0, b) = `(0, "p"/4)`

∴ OA = `"p"/3` and OB = `"p"/4`

Given, A(ΔOAB) = 24 sq. units

∴ `|1/2 xx "OA" xx "OB"|` = 24

∴ `|1/2 xx "p"/3 xx "p"/4|` = 24

∴ p² = 576

∴ p = ± 24