Triangle parallelogram construction

Construct triangle ABC if c = 5 cm, b = 7 cm and a = 4 cm. Then create a parallelogram axially symmetric with the line AC. Measure the size of the second diagonal of this quadrilateral.

Final Answer:

u =  10.247 cm

Step-by-step explanation:

$$\begin{gathered} c=5\text{cm} \\ b=7\text{cm} \\ a=4\text{cm} \\ v=c=5\text{cm} \\ {u}^2+v^2=2\cdot (a^2+b^2) \\ u=\sqrt{2\cdot (a^2+b^2)-v^2}=\sqrt{2\cdot (4^2+7^2)-5^2}=\sqrt{105}=10.247\text{cm} \end{gathered}$$

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