MP Board · Class 9 · Mathematics · Heron's FormulaIf each side of a triangle is doubled, what is the ratio of the area of the new triangle to the area of the given triangle?
Step-by-Step Solution
When sides are doubled ($2a, 2b, 2c$), the semi-perimeter becomes $2s$. The new area is $\sqrt{2s(2s-2a)(2s-2b)(2s-2c)} = \sqrt{16s(s-a)(s-b)(s-c)} = 4 \times \text{Original Area}$. Thus, the ratio is $4:1$.
Detailed Options Breakdown
Option : $2:1$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Heron's Formula.
Option 1: $4:1$ (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 2: $8:1$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Heron's Formula.
Option 3: $1:4$
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.