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Is it possible to construct a quadrilateral ABCD in which AB = 3 cm, BC = 4 cm, CD = 5.4 cm, DA = 5.9 cm and diagonal AC = 8 cm? If not, why?

Solution:

Given, ABCD is a quadrilateral.

AB = 3 cm, BC = 4 cm, CD = 5.4 cm, DA = 5.9 cm and diagonal AC = 8 cm.

We have to determine if it is possible to construct a quadrilateral ABCD.

Consider the △ABC within the quadrilateral.

We know that the sum of two sides of a triangle is always greater than the third side.

AB + BC = 3 + 4

=7 cm

AC = 8 cm

This implies that the sum of two sides of a triangle is less than the third side.

Therefore, it is not possible to construct such a quadrilateral.

✦ Try This: Is it possible to construct a quadrilateral PQRS in which PQ = 5 cm, QR = 3 cm, RS = 3,9 cm, SP = 4.9 cm and diagonal PR = 11 cm? If not, why?

☛ Also Check: NCERT Solutions for Class 8 Maths

NCERT Exemplar Class 8 Maths Chapter 5 Problem 196

Is it possible to construct a quadrilateral ABCD in which AB = 3 cm, BC = 4 cm, CD = 5.4 cm, DA = 5.9 cm and diagonal AC = 8 cm? If not, why?

Summary:

It is not possible to construct a quadrilateral ABCD in which AB = 3 cm, BC = 4 cm, CD = 5.4 cm, DA = 5.9 cm and diagonal AC = 8 cm.

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