Question

If a right angled isosceles triangle right angled at origin has 3x+4y=6 as its base,then the area of the triangle is 6k/25 then k=

Answer 1

The distance from origin to the line gives the height OP of ΔOAB

OP = | [3(0) + 4(0) - 6] |/√(3²+4²) = 6/5 unit

Using RHS axiom of congruence for ΔOAP and ΔOBP

1. ∠OPA = ∠OPB = 90°

2. OP is common side

3. OA = OB (isosceles triangle)

Therefore AP = BP = AB/2

Using pythagorus theorem,

OA² + OB² = AB² implies AB = √2 * OA

OA²= OP² + AP² implies OA² = OP² + OA²/2

i.e OA = √2 * OP

Therefore area of triangle is 1/2 * OA *OB = 1/2 OA² = OP² = 36/25

implies k=6