Question

triangle ABC is similar to triangle PQR, if AB=6, BC=8, CA=10 and QR=6, then what is the length of PR ? ​

Answer 1

Answer:

PR = 15/2 units (OR) 7.5 units

Step-by-step explanation:

∵ triangle ABC is similar to triangle PQR

$\frac{AB}{PQ} = \frac{BC}{QR} =\frac{AC}{PR}$

(i)

$\frac{AB}{PQ} = \frac{BC}{QR}$

⇒ $\frac{6}{PQ} =\frac{8}{6}$

⇒ $\frac{6}{PQ} =\frac{4}{3}$

⇒ $\frac{3}{PQ} =\frac{2}{3}$

⇒ $PQ = \frac{9}{2}$

(ii)

$\frac{AB}{PQ} =\frac{AC}{PR}$

⇒ $\frac{6}{9/2 } =\frac{10}{PR}$

⇒ $\frac{(6)(2)}{9} = \frac{10}{PR}$

⇒ $\frac{2}{3} = \frac{5}{PR}$

⇒ $PR = \frac{15}{2}$