Is it possible to construct a quadrilateral ABCD in which AB=3 CM, BC=

1.	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.
Answer» 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.

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.

Answer»

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.