Question

what is the approximate side length of the square?
3.0 units
3.5 units
4.2 units
4.9 units

Explanation:

Step1: Use Pythagorean theorem

Let the side length of the square be \(a\). The diagonal of the square \(d = 3 + 3=6\). For a square, \(d=\sqrt{2}a\).

Step2: Solve for \(a\)

From \(d = \sqrt{2}a\), we get \(a=\frac{d}{\sqrt{2}}\). Substitute \(d = 6\) into the formula: \(a=\frac{6}{\sqrt{2}}=\frac{6\sqrt{2}}{2}=3\sqrt{2}\approx3\times1.414 = 4.242\approx4.2\)

Answer:

4.2 units