Question

ABCD is a quadrilateral whose one of the diagonal AC bisects it into two triangles equal in area. find the probability that the quadrilateral is chosen has.
1. All the angles are right angles
2.both the diagonals bisect each other
3.diagonal are perpendicular to each other
4. Only one of the diagonals bisect the others.?

Answer 1

Answer:

square

parallelogram

rectangle

rhombus

kite

total no. of outcomes =5

1. 2/5 ( rectangle, square)

2. 4/5 (rectangle, square, parallelogram, rhombus)

Answer 2

Total possible outcomes for a quadrilteral ABCD whose diagonal AC bisects it into two Triangles equal in area are

( paralleogram,square, rectangle,rhombus,kite )

= Total 5

Now,

1)All the angles are right angles = ( rectangle & square) = 2

So, required probability=2/5

2) Both the diagonals bisect each other = ( rectangle,square,paralleogram,rhombus )

So, required probability = 4/5

3) Diagonals are perpendicular to each other = Rhombus , square , kite ,

so, required probability = 3/5

4) Only one of the diagonals bisect the others =

Kite

so, required probability = 1/5

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