Quantitative Aptitude – Geometry – Triangles – Let ABC be a right-angled triangle

Quantitative Aptitude – Geometry – Triangles

Question

Let ABC be a right-angled triangle with BC as the hypotenuse. Lengths of AB and AC are 15 km and 20 km, respectively. The minimum possible time, in minutes, required to reach the hypotenuse from A at a speed of 30 km per hour is

Answer

24

Solution

As per the question from CAT 2017 – Quantitative Aptitude – Geometry – Triangles,
BC^2 = AB^2 + AC^2 = 625
BC = 25
Shortest Distance from A to hypotenuse = altitude on BC = AP
AP * BC = AB * AC
So, AP = 12
Time taken = (12/30) * 60 mins = 24 mins
Answer: 24 mins

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 P be an interior point of a right-angled isosceles triangle ABC with hypotenuse AB.
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