The height of an equilateral triangle of side is 10 3√ cm. calculate its perimeter.

Analyze the question: The question is a little garbled. "10 3√ cm" most likely means the height is 10√3 cm. We need the perimeter of an equilateral triangle with that height.

Concept: For an equilateral triangle of side s, drawing the height splits it into two right-angled triangles (30°-60°-90°). By Pythagoras:

h² = s² − (s/2)² = (3/4)s²

so h = (√3/2) × s

Solution:

1. Set h = 10√3: (√3/2) × s = 10√3

2. Divide both sides by √3: s/2 = 10

3. So s = 20 cm

4. Perimeter = 3 × s = 3 × 20 = 60 cm

Check: With s = 20, h = √(20² − 10²) = √300 = 10√3 ✓

Answer: The perimeter is 60 cm, which is option B.

Tip: Memorize h = (√3/2) × s for equilateral triangles. When the height contains √3, the √3 cancels and the side comes out as a whole number. Don't stop at the side length, because the question asks for the perimeter, and option A (20 cm) is the trap for those who forget to multiply by 3.