Question

In the diagram below, overline QR is parallel to overline NO. PR=8.6, QN=8.6, and RO=6.4. Find the length of overline
PQ. Round your answer to the nearest tenth if necessary.

Answer 1

Let triangle PQR have NO parallel to QR, with N on PQ and O on PR. Then triangles PNO and PQR are similar, so

PN/PQ = PO/PR.

Now PO = PR − RO = 8.6 − 6.4 = 2.2, and PN = PQ − QN = PQ − 8.6. Thus

(PQ − 8.6)/PQ = 2.2/8.6.

Solve for PQ:
1 − 8.6/PQ = 2.2/8.6 → 8.6/PQ = 6.4/8.6 → PQ = 8.6^2/6.4 ≈ 11.55625.

Rounded to the nearest tenth: PQ = 11.6.