Question

similarity transformations
qr, rs, and sq are midsegments of △wxy.
qr = 2.93 cm
rs = 2.04 cm
qs = 2.28 cm
what is the perimeter of △wxy?
12.22 cm
12.46 cm
14.50 cm
11.57 cm

Explanation:

Step1: Recall Midsegment Theorem

The midsegment of a triangle is parallel to the third side and half as long. So, if \( QR \), \( RS \), \( QS \) are midsegments of \( \triangle WXY \), then each side of \( \triangle WXY \) is twice the length of the corresponding midsegment.

Step2: Find lengths of sides of \( \triangle WXY \)

• Side opposite \( QR \): Let's say \( WY = 2 \times QR = 2 \times 2.93 = 5.86 \) cm
• Side opposite \( RS \): Let's say \( WX = 2 \times RS = 2 \times 2.04 = 4.08 \) cm
• Side opposite \( QS \): Let's say \( XY = 2 \times QS = 2 \times 2.28 = 4.56 \) cm

Step3: Calculate Perimeter

Perimeter of \( \triangle WXY \) is \( WY + WX + XY \).
So, \( 5.86 + 4.08 + 4.56 = 14.50 \) cm

Answer:

14.50 cm