Question

The two triangles above are similar.

Answer 1

Answer:

Part a) $x=15\ cm$

Part b) $x=15\ cm$

Part c) The answers are the same because the triangles are similar, therefore the  ratio of their corresponding sides are equal

Step-by-step explanation:

we know that

If two triangles are similar, then the ratio of their corresponding sides are equal  and is called the scale factor

Part a) Find x using the ratio of the sides $12$ cm and $16$ cm

so

$\frac{12}{16}=\frac{x}{20}$

$\frac{3}{4}=\frac{x}{20}$

The ratio of their corresponding sides is called the scale factor and in this problem is equal to $\frac{3}{4}$

solve for x

$x=20*3/4\\x=15\ cm$

Part b) Find x using the ratio of the sides $6$ cm and $8$ cm

so

$\frac{6}{8}=\frac{x}{20}$

$\frac{3}{4}=\frac{x}{20}$

Observe that the scale factor is equal to $\frac{3}{4}$

solve for x

$x=20*3/4\\x=15\ cm$

Part c) The answers are the same because the triangles are similar, therefore the  ratio of their corresponding sides are equal