Solving for the Longest Side: A Step-by-Step Approach **
Introduction: This article will demonstrate a step-by-step approach to solving a geometry problem involving a right-angled triangle, its perimeter, and its area. We will analyze the given information and apply relevant formulas to determine the length of the longest side. Sections: ① Understanding the Problem: We are given the perimeter and area of a right-angled triangle. Our goal is to find the length of the longest side, which is the hypotenuse. ② Applying Formulas: We will use the formulas for the perimeter and area of a triangle: * Perimeter = sum of all sides * Area = (1/2) * base * height ③ Solving for the Sides: We will use the given information and the formulas to set up a system of equations. Solving this system will give us the lengths of the two shorter sides. ④ Finding the Hypotenuse: Using the Pythagorean theorem (a² + b² = c²), we can calculate the length of the hypotenuse (the longest side) using the lengths of the two shorter sides. ⑤ Conclusion:** By following a logical and systematic approach, we can successfully solve the problem and determine the length of the longest side of the right-angled triangle.