This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Hey makongo, good to see you again. Step 1: Identify the relationship between the side length and diagonal of a square. For a square with side length s and diagonal d, the Pythagorean theorem states: s^2 + s^2 = d^2 2s^2 = d^2 Solving for s: s^2 = (d^2)/(2) s = sqrt((d^2)/(2)) s = (d)/(sqrt(2)) Step 2: Substitute the given diagonal length into the formula. The diagonal length d = 10 cm. s = (10)/(sqrt(2)) Step 3: Rationalize the denominator and simplify. To rationalize the denominator, multiply the numerator and denominator by sqrt(2): s = (10)/(sqrt(2)) × sqrt(2)sqrt(2) s = 10sqrt(2)2 s = 5sqrt(2) The side length of the square is 5sqrt(2) cm. s = 5sqrt(2) cm s ≈ 5 × 1.4142 cm s ≈ 7.071 cm The side length of the square is 5sqrt(2) cm. Send me the next one 📸