Question

qr, rs, and sq are midsegments of δwxy. what is the perimeter of δwxy? qr = 2.93 cm rs = 2.04 cm qs = 2.28 cm options: 11.57 cm, 12.22 cm, 12.46 cm, 14.50 cm

Explanation:

Step1: Recall Midsegment Theorem

The midsegment of a triangle is parallel to the third side and half as long. So, if \( \overline{QR} \), \( \overline{RS} \), \( \overline{SQ} \) are midsegments, then the sides of \( \triangle WXY \) are twice the length of the midsegments.

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

• Side \( WY = 2 \times QR = 2 \times 2.93 = 5.86 \) cm
• Side \( WX = 2 \times RS = 2 \times 2.04 = 4.08 \) cm
• Side \( XY = 2 \times QS = 2 \times 2.28 = 4.56 \) cm

Step3: Calculate perimeter

Perimeter \( = WY + WX + XY = 5.86 + 4.08 + 4.56 \)
\( = 5.86 + 4.08 = 9.94 \); \( 9.94 + 4.56 = 14.50 \) cm

Answer:

14.50 cm (corresponding to the option "14.50 cm")