The ratio of the length of each equal side and the third side of an isosceles triangle is 5:6. If the area of the triangle is √11664 sq.cm., then the length of the third side (in cm ) is:

Correct option is A

Given:
Ratio of equal side to the third side = 5:6
Area of the triangle = √11664 sq.cm.
Formula Used:
Area of an isosceles triangle = $$\frac{1}{2}$$​ × base × height
Height = $$\sqrt{a^2 - (\frac{b}{2})^2}$$​ where 'a' is the equal side and 'b' is the base.
Solution:
Let the equal sides be 5x and the third side (base) be 6x.
Calculate the height of the triangle:
Height = $$\sqrt{(5x)^2 - (3x)^2} = \sqrt{25x^2 - 9x^2} = \sqrt{16x^2} = 4x$$​​
Calculate the area of the triangle:
Area =$$\frac{1}{2} × 6x × 4x = 12x^2$$​​
The given area is √11664 = 108.
Equate the calculated area to the given area:
$$12x^2$$​ = 108
$$x^2$$​ = 9
x = 3
Find the length of the third side:
Third side = 6x = 6 × 3 = 18 cm
Final Answer
So the correct answer is (a)