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.
+526 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 \(=(\sqrt {89})^2\)
\(=89 sq. units\)
