Question

$\overline{qr}$, $\overline{rs}$, and $\overline{sq}$ are midsegments of $\triangle wxy$. what is the perimeter of $\triangle wxy$? $\bigcirc$ 11.57 cm $\bigcirc$ 12.22 cm $\bigcirc$ 12.46 cm $\bigcirc$ 14.50 cm $qr = 2.93$ cm $rs = 2.04$ cm $qs = 2.28$ cm

Explanation:

Step1: Recall midsegment theorem

A midsegment of a triangle is $\frac{1}{2}$ the length of the side it is parallel to. So each side of $\Delta WXY$ is twice the length of the corresponding midsegment.

Step2: Calculate side lengths of $\Delta WXY$

$WX = 2 \times RS = 2 \times 2.04 = 4.08$ cm
$XY = 2 \times QS = 2 \times 2.28 = 4.56$ cm
$WY = 2 \times QR = 2 \times 2.93 = 5.86$ cm

Step3: Sum sides for perimeter

Perimeter = $WX + XY + WY$
<Expression>
$4.08 + 4.56 + 5.86$
</Expression>

Answer:

14.50 cm