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The ratio of sides of a triangle is 3:4:5 and area of the triangle is 72 square unit. Then the area of an equilateral triangle whose perimeter is same as that of the previous triangle is
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- 32√3 square units
- 48√3 square units
- 96 square units
- 60√3 square units
- 32√3 square units
Correct Option: B
Using Rule 1 and 6,
Sides of triangle
Let 3x, 4x and 5x units
Here, (3x)² + (4x)² = (5x)²
∴ It is a right angled triangle.
Now, Area of triangle
| = | × 3x × 4x = 6x² | |
| 2 |
∴ 6x² = 72
| ⇒ x² = | |
| 6 |
⇒ x = 1√2 = 2√3
Perimeter of right angled triangle = 3x + 4x + 5x
= 12x = 12 × 2√3 =24√3 units
∴ Perimeter of equilateral triangle = 24√3 units
| Its side = | = 8√3 | |
| 3 |
| Area = | = × (side)² | |
| 4 |
| = | = × 8√3 × 8√3 | |
| 4 |
= 48√3 sq units.
