Q 4

Let $x$ be the side of a square. We need to find $x^2$ .

Notice that $AB$ is the hypotenuse of a right triangle with sides $2x$ and $\frac {3}{2}x$ . So:

$(2x)^2 + (\frac {3}{2}x)^2 = 100^2$

$\implies 4x^2 + \frac{9}{4}x^2 = 10000$

$\implies \frac {25}{4}x^2 = 10000$

$\implies x^2 = 10000 \times \frac {4}{25} = \boxed{1600\text { }cm^2}$