Question

the diagonal of a square is 10 inches long. what is the length, in inches, of each side of the square?

Explanation:

Step1: Define square side length

Let $s$ = side length of the square.

Step2: Apply Pythagorean theorem

For a square, diagonal $d$ satisfies $d^2 = s^2 + s^2$.
Substitute $d=10$:
$$10^2 = 2s^2$$

Step3: Solve for $s^2$

Calculate $10^2=100$, then isolate $s^2$:
$$s^2 = \frac{100}{2} = 50$$

Step4: Solve for $s$

Take square root of both sides:
$$s = \sqrt{50} = 5\sqrt{2}$$

Answer:

$5\sqrt{2}$ (or approximately 7.07 inches, but the exact value is $5\sqrt{2}$)