Question

Abcd is a square p and q are the midpoints of cd and cb.A triangle is got by joining the p,q,a.What is the probability of falling a dot in triangle apq

Answer 1

area of square is..
${a}^{2}$

We know,
Midpoints divide the side of the square into equal parts.
Therefore, length of one side = x

Area = (2x)^2

4x^2

TRIANGLE:

Area = 1/2 l×b

where,
triangle PCQ = 1/2 x^2

triangle ADP = 1/2 2x^2

triangle ABQ = 1/2 2x^2

Thus the area of Triangle APQ is are of Square - area of all three triangles..

= 4x^2 - ( 5/2x^2)
= 3/2x^2

P(area of triangle APQ) = P(Falling the dot in triangle APQ)

P(area of triangle APQ) is
= (3/2)x^2 × 1/4x^2
= 3/8