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The ratio of length of each equal side and the third side of an isosceles triangle is 3 : 4. If the area of the triangle is 18√5 square units, the third side is
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- 16 units
- 5√10 units
- 8√2 units
- 12 units
- 16 units
Correct Option: D
Using Rule 1 and 3,
Let Sides = 3x, 3x and 4x Semi perimeter
| = | = 5x | |
| 2 |
∴ ∆ = √5x(5x - 3x)(5x - 3x)(5x - 4x)
= √5x × 2x × 2x × x
∴ 2√5x² = 18√5
⇒ x² = 9 ⇒ x = 3
∴ Third side = 4x = 4 × 3 = 12 units
