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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
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- 30√5 : 100
- 32√5 : 100
- 36√5 : 100
- 42√5 : 100
- 30√5 : 100
Correct Option: C
Let the third side of isosceles triangle be x units and side of equilateral triangle be y units. According to the question, 2x + 2x + x = 3y
⇒ 5x = 3y ..... (i)
| Area of equilateral triangle = | y² | |
| 4 |
| AB = 2x ; BD = | units | |
| 2 |
∴ AD = √AB² - BD²
| = √4x² - | ||
| 4 |
| = √ | = | x | ||
| 4 | 2 |
| Area of isosceles triangle ABC = | × x × | x | = | x² | |||
| 2 | 2 | 4 |
| = | × |  | y |  | ² | ||
| 4 | 5 |
| = | y² | |
| 100 |
| ∴ Required ratio = | y² : | y² | = 36√5 : 100 | ||
| 100 | 4 |