Question

The two triangles above are similar.

Find x using the ratio of the sides 12 cm and 16 cm:
x
20

=
12
16

x20=1216
. Show your work.
Find x using the ratio of the sides 6 cm and 8 cm. Show your work.
Explain why the answers to (a) and (b) should be the same.
The two triangles above are similar.
Find x using the ratio of the sides 12 cm and 16 cm:
x
20

=
12
16

x20=1216
. Show your work.
Find x using the ratio of the sides 6 cm and 8 cm. Show your work.
Explain why the answers to (a) and (b) should be the same.

Answer 1

see the explanation in the procedure

Explanation:

we know that

If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

In this problem the two triangles are similar

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

we know that

The sides 12 cm and 16 cm are corresponding sides

The sides x cm and 20 cm are corresponding sides

so

`(12)/(16)=(x)/(20)` ---> because the ratio of the corresponding sides is proportional

solve for x

`x=(12)/(16)(20)=15\ cm`

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

we know that

The sides 6 cm and 8 cm are corresponding sides

The sides x cm and 20 cm are corresponding sides

so

`(6)/(8)=(x)/(20)` ---> because the ratio of the corresponding sides is proportional

solve for x

`x=(6)/(8)(20)=15\ cm`

The answers to (a) and (b) are the same, because the triangles are similar and remember that in similar triangles the ratio of the corresponding sides is proportional