The area of an isosceles triangle ABC is 8√5 cm². In

Solution

Let AB = BC = 'x' cm Area of isosceles triangle = {(c/4) X √(4a² - c²)} [Where 'a' is the length of two equal sides and 'c' is the length of third (unequal) side] 8√5 = (8/4) X {√(4 X x² - 8²)} Or, (4√5) = √(4x² - 64) Squaring both sides. (16 X 5) = 4x² - 64 Or, 144 = 4x² Or, x² = 36 So, x = 6 cm (Since, length cannot be negative therefore, we will take the positive root only) So, required perimeter = 6 + 6 + 8 = 20 cm