Question

finding lengths sketch the figure that is described. find the requested length. round decimals to the nearest tenth. 23. the diagonal of a square is 26 inches. find the length of a side.

Explanation:

Step1: Use Pythagorean theorem

For a square with side length $s$, diagonal $d$ satisfies $s^2 + s^2 = d^2$.
Substitute $d=26$:
$$2s^2 = 26^2$$

Step2: Calculate $26^2$ and simplify

$$2s^2 = 676$$
$$s^2 = \frac{676}{2} = 338$$

Step3: Solve for $s$

$$s = \sqrt{338} = \sqrt{169 \times 2} = 13\sqrt{2}$$
Calculate decimal value: $13\sqrt{2} \approx 13 \times 1.4142 = 18.3846$

Step4: Round to nearest tenth

Round 18.3846 to 18.4

Answer:

18.4 inches