Question

1. find the length of a side of a square whose diago-nal is 16 cm long. round your answer to the nearest tenth.

Explanation:

Step1: Apply Pythagorean theorem

Let the side - length of the square be $a$. In a square, if the diagonal is $d$, by the Pythagorean theorem $d^{2}=a^{2}+a^{2}=2a^{2}$. Given $d = 16$ cm, we have $16^{2}=2a^{2}$.
$$2a^{2}=256$$

Step2: Solve for $a^{2}$

Divide both sides of the equation $2a^{2}=256$ by 2.
$$a^{2}=\frac{256}{2}=128$$

Step3: Solve for $a$

Take the square - root of both sides.
$$a=\sqrt{128}$$
Simplify $\sqrt{128}=\sqrt{64\times2}=8\sqrt{2}\approx8\times1.414 = 11.312$. Rounding to the nearest tenth, $a\approx11.3$ cm.

Answer:

$11.3$ cm