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CAT 1995 — QA Question 1

Basics of TrianglesEasy

ABCD is a square of area 4, which is divided into four non-over lapping triangles as shown in figure. Then the sum of the perimeters of the triangles is

Answer & solution

  • A

    8(2 + 2)

  • 8(1 + 2)

  • C

    4(1 + 2)

  • D

    4(2 + 2)

Solution

Since base of each triangle will be counted once, Sum of perimeters of the triangles = Perimeter of the
square + 2 × (Sum of its diagonals).
But each of the other two sides of the triangles is common to two triangles, so it will be counted twice.
Area of the square = 4, therefore length of its side = 2 and perimeter = 8.
Also its diagonal = 22
So the required perimeter = (8 + 2 × 42) = 8(1 + 2).

CAT 1995 QA Q1: ABCD is a square of area 4, which is divided into four non-over lapping triangles as shown in figure. Then the — Solution | TheCATExam