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
Step 1: The ladder, wall, and ground form a right-angled triangle. The height up the wall is 4 m. The distance from the foot of the ladder to the foot of the wall is 7 m. The length of the ladder l m is the hypotenuse. Step 2: Pythagoras theorem states: In a right-angled triangle, a^2 + b^2 = c^2 where c is the hypotenuse. Step 3: Substitute the lengths: 4^2 + 7^2 = l^2 Step 4: Calculate the squares: 16 + 49 = l^2 Step 5: Simplify: 65 = l^2 Step 6: Solve for l: l = sqrt(65) The length of the ladder is sqrt(65) m. sqrt(65)