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 (√2 – 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(√2-1)
CS = PR
(PC)^2 = (PS)^2 + (CS)^2
On solving, we get, PC = 4√2(√2-1)
So, QC = PC + PQ = 4
Area of a right angled triangle = ½ * Base * Height
So, ½ * AC * BC = ½ * QC * AB
On solving, we get a = 4√2
Area of triangle = ½ * a^2 = 16
Answer: 16

Download CAT 2017 Question Paper with answers and detailed solutions in PDF

CAT 2017 Questions from Quantitative Aptitude – Geometry

Quantitative Aptitude – Geometry – Triangles – Q1: Let ABC be a right-angled triangle with BC as the hypotenuse. Lengths of AB and AC are 15 km and 20 km, respectively.
Quantitative Aptitude – Geometry – Triangles – Q2: From a triangle ABC with sides of lengths 40 ft, 25 ft and 35 ft, a triangular portion GBC is cut off where G is the centroid of ABC.
Quantitative Aptitude – Geometry – Circles – Q1: ABCD is a quadrilateral inscribed in a circle with centre O. If ∠COD = 120 degrees and ∠BAC = 30 degrees, then the value of ∠BCD (in degrees) is
Quantitative Aptitude – Geometry – Circles – Q2: Let ABC be a right-angled isosceles triangle with hypotenuse BC. Let BQC be a semi-circle, away from A, with diameter BC.
Quantitative Aptitude – Geometry – Coordinate – Q1: The points (2, 5) and (6, 3) are two end points of a diagonal of a rectangle. If the other diagonal has the equation y = 3x + c, then c is
Quantitative Aptitude – Geometry – Coordinate – Q2: The shortest distance of the point (½, 1) from the curve y = |x -1| + |x + 1| is
Quantitative Aptitude – Geometry – Mensuration
Quantitative Aptitude – Geometry – Polygons – Ques: Let ABCDEF be a regular hexagon with each side of length 1 cm. The area (in sq cm) of a square with AC as one side is

Other posts related to Quantitative Aptitude – Geometry

Geometry Fundas for CAT Quantitative Aptitude Preparation – Part 1
Geometry Fundas for CAT Quantitative Aptitude Preparation – Part 2
Geometry Basics for CAT – Triangle related questions and problems
Mensuration Basics and 3-Dimensional Geometry Concepts for CAT

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