In an isosceles triangle, the length of each equal side is twice the length of the third side. The ratio of areas of the isosceles triangle and an equilateral triangle with same perimeter is:
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 36√5 : 100
Suppose the length of equal sides of the Isoceles triangle = 4a
So, third side = 4a/2 = 2a
Perimeter of Isoceles triangle = Perimeter of equilateral triangle = 4a + 4a + 2a = 10a
So,
Side of equilateral triangle = 10a/3
Now,
Height of Isoceles triangle
h = √[(4x)2 - (a)2] =√[16a2 - a2] = √15 a
And
Area of Isoceles triangle = [1/2 × 2a × √15 a] = √15 a2
And
Area equilateral triangle = √3/4 × 10/3 × 10/3 × a2 = 25√3/9 a2
Ratio of areas = (√15 a2) : (25/9 × √3a2) = 36√5 : 100