MP Board · Class 9 · Mathematics · Heron's FormulaIf the perimeter of an equilateral triangle is $60\text{ cm}$, what is its area?
Step-by-Step Solution
Perimeter = $60\text{ cm}$, so side $a = \frac{60}{3} = 20\text{ cm}$. Area = $\frac{\sqrt{3}}{4}(20)^2 = 100\sqrt{3}\text{ cm}^2$.
Detailed Options Breakdown
Option : $200\sqrt{3}\text{ cm}^2$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Heron's Formula.
Option 1: $100\sqrt{3}\text{ cm}^2$ (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 2: $50\sqrt{3}\text{ cm}^2$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Heron's Formula.
Option 3: $400\sqrt{3}\text{ cm}^2$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Heron's Formula.
💡 Study Guide: This question tests core syllabus concepts from Heron's Formula. For formulas, key summaries, and mock exam reference guides, read the full Heron's Formula Revision Notes.