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: Let the length of the rectangle be l and the width be w. The perimeter is given by 2(l+w) = 20 cm. This simplifies to l+w = 10 cm. Step 2: The diagonal of the rectangle is given by the Pythagorean theorem: l^2 + w^2 = d^2. We are given that the diagonal d = 8 cm, so l^2 + w^2 = 8^2 = 64 cm^2. Step 3: We need to find the area of the rectangle, which is A = l × w. We know that (l+w)^2 = l^2 + 2lw + w^2. We can substitute the values we have: (10)^2 = (l^2 + w^2) + 2lw. 100 = 64 + 2lw. Step 4: Solve for lw: 100 - 64 = 2lw 36 = 2lw lw = (36)/(2) lw = 18 cm^2. The area of the rectangle is 18 cm^2. A = 18 cm^2 18 cm^2 Mándame la siguiente 📸