Question

the figure below is a square. find the length of side $x$ to the nearest tenth.
(figure of a square with a diagonal labeled 1 and a side labeled $x$)
answer attempt 1 out of 2

Explanation:

Step1: Apply Pythagorean theorem

In a square, the diagonal $d$ and side $x$ satisfy $d^2 = x^2 + x^2$. Here, $d=1$, so:
$$1^2 = 2x^2$$

Step2: Solve for $x^2$

Isolate $x^2$ by dividing both sides by 2:
$$x^2 = \frac{1}{2}$$

Step3: Solve for $x$

Take the square root of both sides:
$$x = \sqrt{\frac{1}{2}} = \frac{\sqrt{2}}{2}$$

Step4: Calculate decimal value

Compute the decimal and round to nearest tenth:
$$x \approx 0.707 \approx 0.7$$

Answer:

0.7