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

`(QR)/(XY)= (PR)/(PY)`

we have

`XY=4\ units`

`PR=2PY\ units`

substitutes

`(QR)/(4)=(2PY)/(PY)`

`(QR)/(4)=2`

`QR=8\ units`

therefore

the answer is

`8\ units`