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    Question

    The base of an isosceles triangle is 20 cm, and the sum

    of the other two sides is 30 cm. Find the area of the triangle.
    A 96 cm² Correct Answer Incorrect Answer
    B 50√5 cm² Correct Answer Incorrect Answer
    C 58√5 cm² Correct Answer Incorrect Answer
    D 70√5 cm² Correct Answer Incorrect Answer

    Solution

    Let the equal sides of the isosceles triangle be x. Given: Base = 20 cm, sum of the other two sides = 30 cm, so 2x = 30, x = 15 cm. Now, the altitude divides the triangle into two right-angled triangles. Using Pythagoras' theorem for one of the right-angled triangles: x² = (20/2)² + h² 15² = 10² + h² 225 = 100 + h² h² = 125 h = √125 = 5√5 cm. Area of the triangle = 1/2 × base × height Area = 1/2 × 20 × 5√5 Area = 50√5 cm². Correct option: B) 50√5 cm².

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