Question

construct a quadrilateral PQRS with PQ=3cm,RS=3cm,PS=7.5cm,PR=8cm and SQ=4cm

Answer 1

Given : Quadrilateral PQRS with PQ = 3 cm RS = 3 cm PS = 7.5 cm and SQ = 4 cm

We know from triangle inequality theorem that sum of any two sides is greater than the third side ,

But here we have PQ = 3 cm PS = 7.5 cm SQ = 4 cm ( AS we get PQS triangle in quadrilateral PQRS where PQ and PS are sides and SQ is diagonal of quadrilateral . )

And

PQ + SQ = 3 + 4 = 7

and

PS = 7.5 , So

PQ + SQ > PS , But that equation is not true for any type of triangle .

Therefore,

We can say that from given information we can't construct quadrilateral PQRS