Question
In a right-angled triangle, the length of the hypotenuse
is 25 cm, and the perimeter is 60 cm. Find the area of the triangle.Solution
Let the sides of the right-angled triangle be a, b, and the hypotenuse c = 25 cm. Given: Perimeter = a + b + c = 60, so a + b + 25 = 60, a + b = 35. Using Pythagoras' theorem: a² + b² = 25² = 625 Now, we solve the system of equations: a + b = 35 a² + b² = 625 Squaring a + b = 35, we get: (a + b)² = 35² = 1225 a² + 2ab + b² = 1225 625 + 2ab = 1225 2ab = 1225 - 625 = 600 ab = 300 Area = 1/2 × ab = 1/2 × 300 = 150 cm² Correct option: B) 150 cm²
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