Question

In ΔPRQ, the midsegment XY¯¯¯¯¯ is 4 units long. What is the length of QR¯¯¯¯¯?

8 units

4 units

10 units

16 units

Answer 1

In this problem we have that

XY is parallel to QR

triangle PQR is similar to triangle PXY

$PY=YR \\PX=XQ$

so

by proportion

$\frac{QR}{XY}= \frac{PR}{PY}$

we have

$XY=4\ units$

$PR=2PY\ units$

substitutes

$\frac{QR}{4}=\frac{2PY}{PY}$

$\frac{QR}{4}=2$

$QR=8\ units$

therefore

the answer is

$8\ units$