Question : If in a $ riangle$ABC, D and E are on the sides AB and AC, such that, DE is parallel to BC and $\frac{AD}{BD}$ = $\frac{3}{5}$. If AC = 4 cm, then AE is:
Option 1: 1.5 cm
Option 2: 2.0 cm
Option 3: 1.8 cm
Option 4: 2.4 cm

Question

Question : If in a $ riangle$ABC, D and E are on the sides AB and AC, such that, DE is parallel to BC and $\frac{AD}{BD}$ = $\frac{3}{5}$. If AC = 4 cm, then AE is:

Option 1: 1.5 cm

Option 2: 2.0 cm

Option 3: 1.8 cm

Option 4: 2.4 cm

Team Careers360 · Accepted Answer

Correct Answer: 1.5 cm

Solution :
Given: $\frac{AD}{BD}$ = $\frac{3}{5}$
In $ riangle$ABC and $ riangle$DBE,
$\angle$BAC = $\angle$DAE (same angle)
$\angle$ADE = $\angle$ABC (corresponding angles)
$\angle$AED = $\angle$ACB (corresponding angles)
By AAA similarity, $ riangle$ABC ~ $ riangle$ADE
⇒ $\frac{AD}{AB}$ = $\frac{AD}{AD+BD}$ = $\frac{3}{3+5}$ = $\frac{3}{8}$
Now, $\frac{AD}{AB}$ = $\frac{AE}{AC}$
⇒ $\frac{3}{8}$ = $\frac{AE}{4}$ [since AC = 4 cm]
⇒ AE = $\frac{3×4}{8}$ = 1.5 cm
Hence, the correct answer is 1.5 cm.

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Question : If in a △ABC, D and E are on the sides AB and AC, such that, DE is parallel to BC and ADBD = 35. If AC = 4 cm, then AE is:Option 1: 1.5 cmOption 2: 2.0 cmOption 3: 1.8 cmOption 4: 2.4 cm

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Question : If in a $△$ ABC, D and E are on the sides AB and AC, such that, DE is parallel to BC and $\frac{A D}{B D}$ = $\frac{3}{5}$ . If AC = 4 cm, then AE is:
Option 1: 1.5 cm
Option 2: 2.0 cm
Option 3: 1.8 cm
Option 4: 2.4 cm