Question

Anyone know the answer with explanation please I would appreciate it!

Answer 1

`\displaystyle QR = 12`

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:

`\displaystyle PS = PR + RS`

Substitute:

`\displaystyle (18) = (15) + RS`

Solve for RS

`\displaystyle RS = 3`

Since RS ≅ PQ:

`\displaystyle RS = PQ = 3`

PS is also the sum of PQ, QR, and RS. Hence:

`PS = PQ + QR + RS`

Since PS = 18 and RS = PQ = 3:

`(18) = (3) + QR + (3)`

Solve for QR:

`QR = 12`

In conclusion, QR measures 12 units.