Question

estimate the side length of a square that has a 9 cm long diagonal. cm

Explanation:

Step1: Use Pythagorean theorem

Let the side length of the square be \(a\). In a square, using the Pythagorean theorem \(a^{2}+a^{2}=d^{2}\), where \(d\) is the diagonal. So \(2a^{2}=d^{2}\). Given \(d = 9\) cm, then \(2a^{2}=81\), and \(a^{2}=\frac{81}{2}=40.5\).

Step2: Find the value of \(a\)

\(a=\sqrt{40.5}\). Since \(\sqrt{36}<\sqrt{40.5}<\sqrt{49}\), \(\sqrt{40.5}\approx6.4\) (because \(6.4^{2}=40.96\) which is close to \(40.5\)).

Answer:

\(6.4\)