10th Class Mathematics Triangles Question Bank MCQs - Triangles

If \[\Delta ABC\tilde{\ }\Delta PQR,\] perimeter of \[\Delta ABC=20cm,\] perimeter of \[\Delta PQR=40cm\] and \[\text{PR}=\text{8 cm},\]then the length of AC is:

A) \[\text{8 cm}\]

B) \[\text{6 cm}\]

C) \[\text{4 cm}\]

D) \[5\,cm\]

Correct Answer: C

Solution :

[c] Since, \[\Delta ABC\tilde{\ }\Delta PQR\]

\[\therefore \,\,\,\,\,\,\,\,\,\frac{AC}{PR}=\frac{\text{Perimeter of }\Delta \text{ABC}}{\text{Perimeter of }\Delta \text{PQR}}\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\frac{AC}{8}=\frac{20}{40}\,\,\,\,\,\,\,\,\,\Rightarrow AC=\frac{20\times 8}{40}=4cm\]