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: Find the top base x. The bottom base is 10 m, left projection is 4 m, right projection is 5 m. x = 10 - 4 - 5 x = 1 x = 1 m. Step 2: Find the height h using the left leg. The left leg 15 m is the hypotenuse of a right triangle with base 4 m. h = sqrt(15^2) - 4^2 Substitute values: h = sqrt(225 - 16) h = sqrt(209) h = sqrt(209) m. Step 3: Find the right leg length. The right leg is the hypotenuse of a right triangle with base 5 m and height sqrt(209) m. Right leg = sqrt(5^2) + (sqrt(209))^2 Substitute values: Right leg = sqrt(25 + 209) Right leg = sqrt(234) Simplify: sqrt(234) = sqrt(9 × 26) = 3sqrt(26) Right leg = 3sqrt(26) m. Step 4: Find the perimeter. Perimeter = x + 10 + 15 + 3sqrt(26) Substitute x = 1 m: Perimeter = 1 + 10 + 15 + 3sqrt(26) Perimeter = 26 + 3sqrt(26) 26 + 3sqrt(26) 26 + 3sqrt(26) meters