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# help geometry

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A square is constructed using the hypotenuse line AC of right triangle ABC as a side, as shown below. Find the area of the square if AB = 5 and BC = 8.

May 3, 2021

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By Pythagoras' Theorem, we can find side AC

$$AC^2=AB^2+BC^2$$

$$AC^2=25+64$$

$$AC^2=89$$

$$AC=\sqrt {89}$$

So now we know the side of square is $$\sqrt {89}$$

∴ Area  $$=(\sqrt {89})^2$$

$$=89 sq. units$$

May 3, 2021