Question

the figure below is a square. find the length of side ( x ) to the nearest tenth.

Explanation:

Step1: Apply Pythagorean theorem

In a square, the diagonal \(x\) and two sides (\(a = \sqrt{7}\)) form a right - triangle. By Pythagorean theorem \(x^{2}=a^{2}+a^{2}\). Substitute \(a = \sqrt{7}\), we get \(x^{2}=(\sqrt{7})^{2}+(\sqrt{7})^{2}\).

Step2: Simplify the equation

\(x^{2}=7 + 7=14\).

Step3: Solve for \(x\)

Take the square root of both sides: \(x=\sqrt{14}\approx3.7\)

Answer:

\(x\approx3.7\)