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 lies in the rhombus
a.1/3
b. 2/3
c. 1/2
d. 1/4

Answer 1

Suppose, the side of the square ABCD is a.

Now, 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 i.e. a

Area of the square=a^2 and

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

Hence,  

The 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

Answer 2

Answer:

1/2

Step-by-step explanation:

Suppose, the side of the square ABCD is a.

Now, 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 i.e. a

Area of the square=a^2 and

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

Hence,  

The 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

Read more on Brainly.in - https://brainly.in/question/5675176#readmore