Question

6.
1. In a AABC, D and E are points on the sides
AB and AC respectively such that DE || BC.
If AD = 2.5 cm, BD = 3.0 cm and AE = 3.75
cm, then find AC.
[CBSE 2006]​

Answer 1

$\sf \: In \: ΔABC \: and \: \: ΔADE$

$\sf∠A=∠A \: \:and \: \: ∠ABC=∠ADE$

$\sf \red{ΔABC∼ΔADE}$

$\sf \: \therefore \: \frac{AB}{AD} = \frac{AC}{AE}$

$\sf \: \sf \implies\frac{2.5 + 3}{2.5} = \frac{AC}{3.15}$

$\sf \: \sf \implies \therefore \: AC = \frac{5.5 \times 3.75}{2.5}$

$\pink{ \sf \implies \sf \bold{ = 8.25}cm}$

Hence This is Answer.