If the sum of the lengths of the diagonals of a square is 24 cm, then what is the length of the side of the square?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(6 \sqrt{2}\) cm
Each diagonal of a square is \(\sqrt2\) times the side (Pythagoras: \(d^2=a^2+a^2\)).
The two diagonals are equal, so each diagonal \(=24\div2=12\,\mathrm{cm}\)
Side, the diagonal divided by \(\sqrt2\): \(\displaystyle \frac{12}{\sqrt2}=\frac{12\sqrt2}{2}=6\sqrt2\,\mathrm{cm}\)