Question

Given that BC and BC' lie on the same ray BY. The ratio of $\frac{BC}{C{C}^{\prime }}$ is 3:5.
What will the ratio of corresponding sides be if triangles ABC and A'BC' are similar?

• A. 5:8
• B. 3:8
• C. 8:5
• D. 8:3

Answer 1

The correct option is B

3:8

Since BC and BC' lie on the same line, the points B, C and C' are collinear.
$\frac{BC}{C{C}^{\prime }}=\frac{3}{5}$

Therefore $\frac{B{C}^{\prime }}{BC}=\frac{BC+C{C}^{\prime }}{BC}$

$\frac{B{C}^{\prime }}{BC}=1+\frac{C{C}^{\prime }}{BC}$

$\frac{C{C}^{\prime }}{BC}=\frac{5}{3}$ (Given)

So, $\frac{B{C}^{\prime }}{BC}=\frac{8}{3}$

Therefore, the ratio of corresponding sides i.e. $\frac{BC}{B{C}^{\prime }}$ is $\frac{3}{8}$.