Question

Find the length of MN​

Answer 1

• The length of MN is 5 cm

Explanation:

Add the segment LX, parallel to QP.

Recall the properties of midsegment:

• Midsegment is parallel to side,
• Midsegment is half the length of the parallel side.

We have:

• Since QL = LR, the point L is midpoint of Q,
• Since PN = NL, the point N is midpoint of PL,
• Since LX is parallel to QP, LX is midsegment of ΔPRQ.

Find the length of LX:

• LX = QP/2 = 20/2 = 10 cm

Since QP ║ LX ║ NM, the segment NM is the midsegment of ΔPLX.

Find the length of NM:

• NM = LX/2 = 10/2 = 5 cm