NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 6: Triangles - Exercise 6.3

Question 6

Step 1: In an equilateral triangle, all three sides are equal and all angles are 60°.

Step 2: The altitude (height) of an equilateral triangle divides it into two equal right-angled triangles.

Step 3: Formula for altitude of an equilateral triangle is:

\[ h = \dfrac{\sqrt{3}}{2} \times a \]

where \(a\) = length of each side.

Step 4: Here, \(a = 8\,\text{cm}\).

So,

\[ h = \dfrac{\sqrt{3}}{2} \times 8 \]

Step 5: Simplify:

\[ h = 4\sqrt{3}\,\text{cm} \]

Final Answer: The altitude is \(4\sqrt{3}\,\text{cm}\).