Question

In ΔABC and ΔPQR, ABC⇔QPR is a similarity. The perimeter of ΔABC is 15 and perimeter of ΔPQR is 27. If BC=7 and QR=9, find PR and AC.

Answer 1

Answer:

AC =3 & PR = 5.4  ( assuming PQ = 9 instead of QR = 9)

Step-by-step explanation:

ABC⇔QPR is a similarity

The perimeter of ΔABC is 15 and perimeter of ΔPQR is 27

=> AB/PQ  = BC/QR  = AC/PR  = (AB + BC + AC)/(PQ + QR + PR ) = 15/27 = 5/9

Given  BC = 7   => 7/QR = 5/9  => QR = 12.6

but given QR = 9 this mean data is wrong

Assuming PQ = 9  Then AB/9 = 5/9 => AB = 5

AB = 5  BC = 7  => AC = 12 - 5 - 7 = 3

PR = 27 - 9 - 12.6 = 5.4

AC =3 & PR = 5.4