Question

qr, \\(\overline{rs}\\), and \\(\overline{sq}\\) are midsegments of \\(\delta wxy\\). what is the perimeter of \\(\delta wxy\\)? \\(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 \( QR \), \( RS \), \( QS \) are midsegments, then the sides of \( \triangle WXY \) are twice the length of the midsegments.
Let the sides of \( \triangle WXY \) be \( WX \), \( XY \), \( YW \). Then:

• \( WX = 2 \times RS = 2\times2.04 = 4.08 \) cm (since \( RS \) is midsegment parallel to \( WX \))
• \( XY = 2 \times QS = 2\times2.28 = 4.56 \) cm (since \( QS \) is midsegment parallel to \( XY \))
• \( YW = 2 \times QR = 2\times2.93 = 5.86 \) cm (since \( QR \) is midsegment parallel to \( YW \))

Step2: Calculate Perimeter

Perimeter \( P \) of \( \triangle WXY \) is \( P = WX + XY + YW \)
\( P = 4.08 + 4.56 + 5.86 \)
\( P = 14.50 \) cm

Answer:

14.50 cm