In a quadrilateral ABCD, AB = 7 cm, BC = 5 cm, AC = 9 cm, AD = 6 cm, CD = 2 cm. Which of the following options is true about the construction of a quadrilateral ABCD?

It is possible to draw the quadrilateral

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It is not possible to draw the quadrilateral since AD + DC < AC

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It is possible to draw the quadrilateral since AD + DC < AC

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None of these

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Solution

The correct option is B It is not possible to draw the quadrilateral since AD + DC < AC
In a triangle, sum of any two sides should be greater than the third side. A quadrilateral is made up of two triangles.

It is given that AD = 6 cm, CD =2 cm and AC = 9 cm. AC $>$ AD + CD. This does not satisfy triangle inequality and hence the quadrilateral ABCD cannot be drawn.

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