PQR is an equilateral triangle. MN is drawn parallel to

Home » Aptitude » Plane Geometry » Question

PQR is an equilateral triangle. MN is drawn parallel to QR such that M is on PQ and N is on PR. If PN = 6 cm, then the length of MN is

1. 3 cm
2. 6 cm
3. 12 cm
4. 4.5 cm

Correct Option: B

We draw a figure an equilateral triangle PQR , in which MN is drawn parallel to QR such that M is on PQ and N is on PR ,

MN || QR
∴ ∠PMN = ∠PQR
∠PNM = ∠PRQ
By AA-similarity,
∆PMN ~ ∆PQR
∠PMN will also be an equilateral triangle.
∴ MN = PN = PM = 6 cm. { ∴ PN = 6 cm }