CAT 2017 Question Paper | Quants Slot 2

CAT Previous Year Paper | CAT Geometry Questions | Question 20

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Question 20 : 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 - 1) cm, then the area, in sq. cm, of the triangle ABC is [TITA]


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Explanatory Answer

Method of solving this CAT Question from Geometry
CAT 2017 Question Paper Quants Slot 2 Geometry

Let ABC be the right angled isosceles triangle with hypotenuse AB and P be an interior point
r (inradius) = 4(√2 - 1)
In any right triangle with a , b , h being its sides, r = \\frac{a + b - h}{2})
Here we have the right angled isosceles triangle with a , a , a√2 as its sides
⟹ r = \\frac{a + a - a√2}{2}) = 4(√2 - 1)
⟹ \\frac{2a - √2a}{2}) = 4(√2 - 1)
⟹ \\frac{√2a(√2 - 1)}{2}) = 4(√2 - 1)
⟹ \\frac{a}{√2}) = 4
⟹ a = 4√2
⟹ The area of the triangle ABC = \\frac{1}{2}) × 4√2 × 4√2
The area of the triangle ABC = 16 sq.cm

The question is "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 - 1) cm, then the area, in sq. cm, of the triangle ABC is [TITA]"

Hence, the answer is 16

 

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