10 POINTS PLEASE HELP
The perimeter of △PQR is 44 cm, and △PQR ~ △WXY. If PQ = 12 and XY + WY = 24, what is the perimeter of WXY? Complete the explanation.

Since the perimeter of △PQR = 44, QR + PR = 44 − PQ, or __ cm. This is proportional to the sum XY + WY, because the two triangles are (similar or congruent)
so their corresponding sides are (not proportional or proportional). Their ratio is 24: , or 3: , which is the same ratio as their perimeters, 3/_ = P/44, so P = ___ cm.

Since the perimeter of ΔPQR = 44, QR + PR = 44 - PQ, or 32 cm. This is proportional to the sum XY + WY, because the two triangles are similar so their corresponding sides are proportional. Their ratio is 24:32 or 3:4, which is the same as their perimeters, 3/4 = P/44, so P = 33 cm.

Step-by-step explanation:

The given parameters are;

ΔPQR ~ ΔWXY

Perimeter of ΔPQR = 44

PQ = 12

XY + WY = 24 based on position is proportional to QR + PR

However, the perimeter of ΔPQR = PQ + QR + PR = 44

Therefore, QR + PR = 44 - PQ = 44 - 12 = 32

Hence, XY + WY = 24 based on position is proportional to QR + PR = 32

If XY:QR = WY:PR we get (XY + WY):(QR + PR) (common factors)

∴ (XY + WY):(QR + PR) = 24:32 = 3:4

By extension, (WX + XY + WY):(PQ + QR + PR) = 3:4

Where: WX + XY + WY = P and PQ + QR + PR = 44 we have;

P:44 = 3:4 or 3/4 = P/44

From which P = 44 × 3/4 = 33 cm.