Question

Statement (1): In the given diagram, OAB is an equilateral triangle. Co-ordinates of the vertex B = (4, 4).

Statement (2): B = (4, `4sqrt3`)

Options

• Both the statements are true.

• Both the statements are false.

• Statement 1 is true, and statement 2 is false.

• Statement 1 is false, and statement 2 is true.

Answer 1

Statement 1 is false, and statement 2 is true.

Explanation:

In the equilateral triangle OAB with side length 8 units on the x-axis starting from the origin O, the vertex B has an x-coordinate of 4 (midpoint of the base) and a y-coordinate given by the height of the equilateral triangle:

\[h = \frac{\sqrt{3}}{2} \times \text{side} = \frac{\sqrt{3}}{2} \times 8 = 4\sqrt{3}\]

Thus, B = (4, `4sqrt3`), making Statement 1 false and Statement 2 true.