Is it possible to construct a quadrilateral A B C D in which A B=… - Vidyadip

Question

Is it possible to construct a quadrilateral $A B C D$ in which $A B=3 cm, B C=4 cm, C D=5.4 cm, D A=5.9 cm$ and diagonal $A C=8 cm$ ? If not, why?

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Answer

No, Given measures are $A S=3 cm, SC =4 cm, C D=5.4 cm$, $DA =59 cm$ and $AC =8 cm$
Here, we observe that $A S+S C=3+4=7 cm$ and $A C=8 cm$
i.e. the sum of two sides of a triangle is less than the third side, which is absurd.
Hence, we cannot construct such a quadrilateral.

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