Question:
Construct a quadrilateral ABCD, when AB = 3 cm, CD = 3 cm, DA = 7.5 cm, AC = 8 cm and BD = 4 cm.
Solution:
If we consider a triangle ABD from the given data, then
AB = 3 cm
BD = 4 cm
AD = 7.5 cm
AB + BD = 3 + 4 = 7 cm
However, we know that the sum of the lengths of two sides of a triangle is always greater than the third side.
Therefore, construction is not possible from the given data.