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Triangles
RD Sharma
CBSE
Grade 10
Question:
In $\Delta ABC$, $D, E, F$ are midpoints of sides $AB, BC, CA$ respectively. Find the ratio of perimeters of $\Delta DEF$ and $\Delta ABC$.
Step-by-Step Solution
Key Concept: By Midpoint Theorem: $DE = (1/2)AC, EF = (1/2)AB, FD = (1/2)BC$. Perimeter of $\Delta DEF = (1/2)(AB + BC + CA) = (1/2)$ Perimeter of $\Delta ABC$. Ratio is $1 : 2$.
By Midpoint Theorem, $DE = \dfrac{1}{2}AC, EF = \dfrac{1}{2}AB, FD = \dfrac{1}{2}BC$. [1.0 Mark] Perimeter of $\Delta DEF = DE + EF + FD = \dfrac{1}{2}(AC + AB + BC) = \dfrac{1}{2} \text{Perimeter}(\Delta ABC)$. [1.0 Mark] Ratio is $1 : 2$. [1.0 Mark]
--- 🎯 Official CBSE Marking Scheme: Applying Midpoint Theorem: 1.0 Mark Expressing perimeter of $\Delta DEF$ as half of $\Delta ABC$: 1.0 Mark Concluding ratio $1 : 2$: 1.0 Mark
Correct Answer:
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