Question

Construct a ΔPQR such that QR = 6.5 cm, ∠P = 60° and the altitude from P to QR is of length 4.5 cm.

Answer 1

Construction:

Steps (1) Draw QR = 6.5 cm.

Steps (2) Draw ∠RQE = 60°.

Steps (3) Draw ∠FQE = 90°.

Steps (4) Draw ⊥^r bisector to QR.

Steps (5) The ⊥^r bisector meets QF at O.

Steps (6) Draw a circle with O as centre and OQ as raidus.

Steps (7) Mark an arc of 4.5 cm from G on the ⊥^r bisector. Such that it meets LM at N.

Steps (8) Draw PP’ || QR through N.

Steps (9) It meets the circle at P, P’.

Steps (10) Join PQ and PR.

Steps (11) ΔPQR is the required triangle