Triangles
RD Sharma
CBSE
Grade 10
Question:
In $\Delta ABC$, $DE \parallel BC$ such that $AD = 2.5\text{ cm}, DB = 3\text{ cm}, AE = 3.75\text{ cm}$. Find $EC$ and $AC$.
Step-by-Step Solution
Key Concept: $\dfrac{2.5}{3} = \dfrac{3.75}{EC} \Rightarrow EC = \dfrac{3 \times 3.75}{2.5} = 4.5\text{ cm}$. $AC = 3.75 + 4.5 = 8.25\text{ cm}$.
By BPT, $\dfrac{2.5}{3} = \dfrac{3.75}{EC} \Rightarrow EC = \dfrac{11.25}{2.5} = 4.5\text{ cm}$. [1.5 Marks]
$AC = AE + EC = 3.75 + 4.5 = 8.25\text{ cm}$. $EC = 4.5\text{ cm}, AC = 8.25\text{ cm}$. [1.5 Marks]
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🎯 Official CBSE Marking Scheme:
Calculating $EC = 4.5\text{ cm}$: 1.5 Marks
Calculating $AC = 8.25\text{ cm}$: 1.5 Marks
Correct Answer:
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