Answer:
[tex]\displaystyle QR = 12[/tex]
Step-by-step explanation:
First, it's never a bad idea to draw the line and see what it looks like! This is shown below (not to scale).
We are given that PS = 18 and PR = 15, and we want to determine QR.
PS is the sum of PR and RS:
[tex]\displaystyle PS = PR + RS[/tex]
Substitute:
[tex]\displaystyle (18) = (15) + RS[/tex]
Solve for RS
[tex]\displaystyle RS = 3[/tex]
Since RS ≅ PQ:
[tex]\displaystyle RS = PQ = 3[/tex]
PS is also the sum of PQ, QR, and RS. Hence:
[tex]PS = PQ + QR + RS[/tex]
Since PS = 18 and RS = PQ = 3:
[tex](18) = (3) + QR + (3)[/tex]
Solve for QR:
[tex]QR = 12[/tex]
In conclusion, QR measures 12 units.
