Question

the two triangles above are similar.

a. find x using the ratio of the sides 12 cm and 16 cm: x/20 = 12/16. show your work.

b. find x using the ratio of the sides 6 cm and 8 cm show your work.

c. explain why the answers to (a) and (b) should be the same.

if someone could please answer this as fast as they can with the answer and the work, that would be great, thank you.

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