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If the numerical values of the height and the area of an equilateral triangle be same, then the length of each side of the triangle is
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- 2 units
- 4 units
- 5 units
- 8 units
- 2 units
Correct Option: A
AB = 2x units
BD = DC = x units
AD = √AB² - BD²
= √4x² - x²
= √3x²
= √3x units
| Area of ∆ABC = | × (2x)² | |
| 4 |
According to question,
| ∵ | × (2x)² = √3x | |
| 4 |
| ⇒ | × 4x² = √3x | |
| 4 |
⇒ x² = x ⇒ x (x – 1) = 0
⇒ x = 1 Hence length of side 2 × 1 = 2 units
∴ Length of side = 9 units
