The ratio of BCCC′ is 3:5. What will the ratio of corresponding sides be if t

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The ratio of $\frac{B C}{C C^{'}}$ 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.

Options:

A . 5:8

B . 3:8

C . 8:5

D . 8:3

Answer: Option B
:
B

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

Therefore $\frac{B C^{'}}{B C}$ = $\frac{B C + C C^{'}}{B C}$

$\frac{B C^{'}}{B C}$ = 1+ $\frac{C C^{'}}{B C}$

$\frac{C C^{'}}{B C}$ = $\frac{5}{3}$ .

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

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

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