Question

Find the perimeter of $\Delta ABC$ if AC || RP?

• A. 50cm
• B. 54cm
• C. 48cm
• D. 40cm

Answer 1

The correct option is B

54cm

According to Basic Proportionality Theorem, if a line is drawn parallel to any sides of the triangle, then it divides other two sides of the triangle proportionally.

Here, RP || AC

$\therefore \frac{BR}{AR}=\frac{BP}{CP}$

On substituting the values we get:

$\frac{7}{14}=\frac{BP}{10}$

$BP=\frac{7\times 10}{14}=\frac{70}{14}=5cm$

$\therefore$ Perimeter of $\Delta ABC$ = AB + BC + AC = 18cm + 21cm + 15cm = 54cm