Question

Let P be an interior point of a right-angled isosceles triangle ABC with hypotenuse AB. If the perpendicular distance of P from each of AB, BC, and CA is 4 (√2 - l) cm, then the area, in sq cm, of the triangle ABC is

• A. 10
• B. 19
• C. 18
• D. 16

Answer 1

The Correct Option is D

As P is equidistant from the sides, P is the in center of the triangle.
r is the in radius of the triangle, viz. 4(√2 - 1) cm
Let the sides of the triangle be a, a, a √2
As Δ=1/2 (a)(a) = r(s),
a2/2 = 4(√2-1)(a+a+a√2)/2
⇒ a = 4√2
Area = 1/2(a2) = 16 sq.units