CBSE2026Class Class 10 · Mathematics1 Marks · Mcq✅ Verified
In the given figure, $DE \parallel BC$. If $\dfrac{AD}{DB}=\dfrac{1}{3}$ and $AC = 6$ cm, then length AE is
A. $1.5$ cm
B. $1$ cm
C. $2$ cm
D. $3$ cm
✅ Answer & Solution
✅ Correct Answer: A
Step 1: Since $DE\parallel BC$, by Basic Proportionality (Thales) Theorem:
$$\frac{AD}{DB}=\frac{AE}{EC}=\frac{1}{3}$$
Step 2: Let $AE=x$, then $EC=3x$.
Step 3: $AC=AE+EC=x+3x=4x$.
Step 4: Given $AC=6$ cm, so $4x=6\Rightarrow x=1.5$ cm.
Answer: (A) $AE=1.5$ cm
