we have two similar triangles.
we know that in similar traingles ratios of the corresponding sides are always equal.
we have AB is propotional to PQ
BC is propotional to QR
AC is propotionbal to PR
here we dont have the lengths of sides
[tex] PQ/AB=QR/BC=PR/AC=k
[/tex]
so the length of PR and QR will be equal to some constant have same value .
Answer: PR = 20; QR = 25
Step-by-step explanation: Similar triangles means the triangles have their sides proportional to one another.
In the picture from attachment, Triangle ABC has sides:
AB = 9
BC = 15
AC = 12
Triangle PQR is proportional to ABC, which means:
AB is proportional to PQ
AC is proportional to PR
Bc is proportional to QR
Or,
[tex]\frac{PQ}{AB} = \frac{PR}{AC} = \frac{QR}{BC}[/tex]
PQ, AB and AC is known, so calculate PR:
[tex]\frac{15}{9}=\frac{PR}{12}[/tex]
PR = [tex]\frac{15.12}{9}[/tex]
PR = 20
With PR, find QR:
[tex]\frac{15}{9} = \frac{QR}{15}[/tex]
QR = [tex]\frac{15.15}{9}[/tex]
QR = 25
QR measures 25 and PR measures 20
