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
Here's how to find the length of OP using the Pythagorean theorem. Step 1: Identify the knowns and the unknown in the right-angled triangle. The triangle has a right angle at O. The length of side OQ is 2 cm. The length of the hypotenuse QP is 4 cm. We need to find the length of side OP. Step 2: Apply the Pythagorean theorem. The Pythagorean theorem states that a^2 + b^2 = c^2, where a and b are the lengths of the two shorter sides and c is the length of the hypotenuse. In this triangle: OQ^2 + OP^2 = QP^2 Step 3: Substitute the known values into the equation. (2 cm)^2 + OP^2 = (4 cm)^2 4 cm^2 + OP^2 = 16 cm^2 Step 4: Solve for OP^2. OP^2 = 16 cm^2 - 4 cm^2 OP^2 = 12 cm^2 Step 5: Find the length of OP by taking the square root. OP = sqrt(12 cm)^2 OP = sqrt(4 × 3) cm OP = 2sqrt(3) cm The length of OP is 2sqrt(3) cm. 3 done, 2 left today. You're making progress.