Question

the figure is a square. its diagonals meet to form four right angles. what is the approximate value of x?
2.8 units
3.3 units
4.0 units
5.7 units

Explanation:

Step1: Recall property of square diagonal

In a square of side length \(s = 8\), the length of the diagonal \(d\) is given by the Pythagorean theorem \(d=\sqrt{s^{2}+s^{2}}\).
\[d=\sqrt{8^{2}+8^{2}}=\sqrt{64 + 64}=\sqrt{128}=8\sqrt{2}\]

Step2: Diagonal - half length relationship

The diagonals of a square bisect each other at right - angles. The value of \(x\) is half of the diagonal length. So \(x=\frac{d}{2}\).
\[x=\frac{8\sqrt{2}}{2}=4\sqrt{2}\approx4\times1.414 = 5.656\approx5.7\]

Answer:

5.7 units