Length of diagonal of the square is :

The correct answer is Option (1) → \(14\sqrt{2}\) cm

O is the centre of AD and OE is a radius of the semicircle drawn on AD, so the side of the square is AD, \(2\times7=14\) cm. A diagonal divides the square into two right triangles, so by Pythagoras the diagonal of a square is its side times \(\sqrt{2}\).

• In the right triangle ABC: \(AC^{2}=AB^{2}+BC^{2}=14^{2}+14^{2}=2\times14^{2}\)

• Diagonal \(AC=14\sqrt{2}\) cm