Question
The area of an isosceles triangle ABC is 8√5 cm
2 . If AB = BC and AC = 8 cm, then find the perimeter of triangle ABC.Solution
Let AB = BC = 'x' cm
Area of isosceles triangle = {(c/4) X √(4a 2 - c 2 )} [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 x 2 - 8 2 )}
Or, (4√5) = √(4x 2 - 64)
Squaring both sides.
(16 X 5) = 4x 2 - 64
Or, 144 = 4x 2
Or, x 2 = 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
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