Question

The length of the diagonal of a square and that of the side of another square are both 10 cm. What is the ratio of the area of the first square to that of the second?

• A. $1:2$
• B. $2:1$
• C. $\sqrt{2}:1$
• D. $1:\sqrt{2}$

Answer 1

The correct option is A $1:2$

Length of diagonal of first square$=10cm$

$\therefore$Side of first square$=\frac{d}{\sqrt{2}}=\frac{10}{\sqrt{2}}=\frac{10\sqrt{2}}{2}=5\sqrt{2}cm$

Area of first square$={\left(5\sqrt{2}\right)}^2=50m^2$

$=10cm$

Area of second square$={\left(10\right)}^2=100m^2$

Now, $\frac{Areaoffirstsquare}{Areaofsecondsquare}=\frac{50m^2}{100m^2}=1:2$