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.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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