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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