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Question

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


Solution

Given measures are 
$$AB  = 3\text{ cm}  , BC  = 4\text{ cm}, CD  = 5.4\text{ cm}, DA = 5.9\text{ cm}$$ and $$AC = 8\text{ cm}$$ 

Here, consider the $$\triangle ABC$$ within the quadrilateral.
$$AB + BC  = 3 + 4 = 7\text{ cm} $$ and $$AC  = 8\text{ cm} $$ 
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. 

Maths

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