Is it possible to construct a quadrilateral ABCD in which AB=3 CM, BC=4 CM, CD=5.5 CM,DA=6 CM and BD=9 CM? If not, give reason.
Answers
No. We cannot construct this quadrilateral.
Reason:
First we have to draw ∆ABD and after that we can continue to join BC and CD.
By triangle property, sum of any two sides of a triangle is always greater than the third side. Then only we can draw a triangle.
But, in the given sum, to draw ∆ABD,
AB + AD = 3 + 6 = 9 cm which is equal to third side BD, 9 cm.
According to triangle property, third side is not grater than the sum of the other two sides.
Hence, we cannot construct ∆ as well as the quadrilateral based on the given measurements.
Answer:
Given measures are
AS=3cm,BC=4cm,CD=5.4cm,DA=59cm and AC=8cm
Here, consider the triangle ABC within the quadrilateral.
AB+BC=3+4=7cm and AC =8cm
i.e., the sum of two sides of a triangle is less than the third side, which is absurd.
Hence, we cannot construct such a quadrilateral.