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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

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