Question

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? Given that BC and BC' lie
on the same ray BY.

• 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+ $\frac{C{C}^{\prime }}{BC}$

$\frac{C{C}^{\prime }}{BC}$ = $\frac{5}{3}$.

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

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

The ratio of corresponding sides of triangles $ABC$ and $A^{\prime }B{C}^{\prime }$ =$\frac{3}{8}$