The diagonal of a square is \(4\sqrt{2}\) cm. The diagonal of another square whose area is double that of the first square, is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 8 cm
The diagonal of a square of side \(a\) is \(a\sqrt{2}\), so area \(=\frac{1}{2}\times(\text{diagonal})^2\). The area of the first square gives the area, and then the diagonal, of the second.
Area of the first square \(\displaystyle =\frac{1}{2}\times\left(4\sqrt{2}\right)^2=\frac{1}{2}\times32=16\) cm2
Area of the second square \(=2\times16=32\) cm2
\(\displaystyle \frac{1}{2}\times(\text{diagonal})^2=32\), so \((\text{diagonal})^2=64\) and the diagonal is 8 cm
Shortcut: Area grows as the square of the diagonal, so doubling the area multiplies the diagonal by \(\sqrt{2}\).
New diagonal \(=4\sqrt{2}\times\sqrt{2}=8\) cm