Quantitative Aptitude – Geometry – Triangles – Let P be an interior point

Quantitative Aptitude – Geometry – Triangles

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 (âˆš2 – l) cm, then the area, in sq cm, of the triangle ABC is

Answer

16

Solution

From CAT 2017 – Quantitative Aptitude – Geometry – Triangles, we can see that,

PQ = PR = PS = 4(âˆš2-1)
CS = PR
(PC)^2 = (PS)^2 + (CS)^2
On solving, we get, PC = 4âˆš2(âˆš2-1)
So, QC = PC + PQ = 4
Area of a right angled triangle = Â½ * Base * Height
So, Â½ * AC * BC = Â½ * QC * AB
On solving, we get a = 4âˆš2
Area of triangle = Â½ * a^2 = 16
Answer: 16

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