Question

Abcd is a square. Pqrs is a rhombus lying inside the square such that p, q, r and s are the mid-points of ab, bc, cd and da respectively. A point is selected at random in the square. Find the probability that it lies in the rhombus. (a) 1/3 (b) 2/3 (c) 1/2 (d) 1/4

Answer 1

Since the rhombus lying inside is made by the mid-points of AB, BC, CD and DA, the diagonals of the rhombus will be equal to the sides of the square (say a)

now, Area of the square=a^2

Area of the rhombus=1/2 X product of diagonals = (1/2)a^2

Therefore, probability of selected point to lie inside the rhombus= area of rhombus/area of square

=1/2

Therefore, option c is correct i.e. 1/2