Question

$\text{In the given figure, DE || BC. If AD = 6 cm,}\text{AB = 24 cm and DE = 5 cm, then}\text{BC = \_\_\_\_ cm.}$

• A. 20
• B. 5
• C. 10
• D. 24

Answer 1

The correct option is A

20

$\text{Consider}\Delta ADE\text{and}\Delta ABC,DE||BC\text{(Given)}$

$\angle ADE=\angle ABC\angle AED=\angle ACB\text{(Corresponding angles are equal)}$

$\angle DAE=\angle BAC\text{(Common angle)}$

$\therefore △ADE\sim △ABC\text{(AA Similarity)}$
$\text{So,}\frac{DE}{BC}=\frac{AD}{AB}$

$\Rightarrow BC=\frac{DE\times AB}{AD}$

$\Rightarrow BC=\frac{5\times 24}{6}$

$\Rightarrow BC=20cm$