Question

M and N are mid points of AB and AC of ΔABC. AB = 9 cm, BC = 12 cm. Perimeter of BPNM is ______.

Options

• 20 cm

• 18 cm

• 21 cm

• 19 cm

Answer 1

M and N are mid points of AB and AC of ΔABC. AB = 9 cm, BC = 12 cm. Perimeter of BPNM is 21 cm.

Explanation:

Given:

• In ΔABC, M and N are midpoints of AB and AC respectively.
• AB = 9 cm
• BC = 12 cm
• We need to find the perimeter of quadrilateral BPNM, where P lies on BC such that PN is parallel to AB.

Since M and N are midpoints of AB and AC respectively, segment MN is the mid-segment of triangle ABC and is parallel to BC.

Because M and N are midpoints, MN = `1/2` × BC = `1/2` × 12 = 6 cm.

P is the midpoint of BC (since in the figure PN is drawn parallel to AB, and by midpoint theorem, it implies P is midpoint), so BP = PC = `12/2` = 6 cm.

Quadrilateral BPNM consists of segments:

• BM: Since M is midpoint of AB, BM = `1/2` × AB = `1/2` × 9 = 4.5 cm
• PN: PN is parallel to AB and equals BM = 4.5 cm (by the properties of parallelogram formed)
• MN: As calculated, MN = 6 cm
• BP: As P is midpoint of BC, BP = 6 cm

Therefore, perimeter of BPNM

= BM + MN + PN + BP

= 4.5 + 6 + 4.5 + 6

= 21 cm

The perimeter of quadrilateral BPNM is 21 cm.