Question

$\text{In the figure given below, point D divides}\text{AB in the ratio 3 : 5 and DE is parallel to}\text{BC. If AE = 4.8 cm, then find the}\text{length of AC.}$

• A. $8.8cm$
• B. $12.8cm$
• C. $4.8cm$
• D. $12cm$

Answer 1

The correct option is B

$12.8cm$

$\text{In}\Delta ABC,DE||BC\text{(Given)}$

$\text{Since point D divides AB in the ratio}\text{3 : 5.}$

$\text{So, AD : DB = 3 : 5}$

$\text{By basic proportionality theorem,}\frac{AD}{DB}=\frac{AE}{EC}$

$\frac{3}{5}=\frac{4.8}{EC}$

$EC=\frac{4.8\times 5}{3}$

$\Rightarrow EC=8$

$\text{Now, AC = AE + EC}$

$\Rightarrow AC=4.8+8=12.8cm$