MP Board · Class 10 · Mathematics · TrianglesIf triangle ABC is similar to triangle DEF such that BC = 3 cm, EF = 4 cm and area of triangle ABC = 54 sq cm, then the area of triangle DEF is:
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Total Attempts: 4
Accuracy Rate: 25%
Step-by-Step Solution
The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. Area(ABC)/Area(DEF) = (BC/EF)^2. Therefore, 54/Area(DEF) = (3/4)^2 = 9/16. Area(DEF) = (54 * 16) / 9 = 6 * 16 = 96 sq cm.
Detailed Options Breakdown
Option : 72 sq cm
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Triangles.
Option 1: 96 sq cm (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 2: 108 sq cm
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Triangles.
Option 3: 64 sq cm
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Triangles.
💡 Study Guide: This question tests core syllabus concepts from Triangles. For formulas, key summaries, and mock exam reference guides, read the full Triangles Revision Notes.