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If the difference between areas of the circumcircle and the incircle of an equilateral triangle is 44 cm2, then the area of the triangle is (Take π = 22/7)
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- 28 cm²
- 7√3 cm²
- 14√3 cm²
- 21 cm²
- 28 cm²
Correct Option: C
Let the each side of the equilateral triangle be 2x cm.
Then BD = x
| Radius of incircle = OD = | AD | |
| 3 |
| = | √(2x)² - x² | |
| 3 |
| = | = | cm | ||
| 3 | √3 |
Radius of circum circle = BO = √BD² + OD²
| = √x² + | = | cm | ||
| 3 | √3 |
According to the question,
| π |  |  | ² | - | π | | | ² | = 44 | ||
| √3 | √3 |
| ⇒ | - | = 44 | ||
| 3 | 3 |
⇒ πx² = 44
| ⇒ x² = | = 14 | |
| 22 |
∴ Area of the equilateral triangle
| = | × side² = | ×(2x)² | ||
| 4 | 4 |
= √3 x² = 14√3 Sq. cm.
