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

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

Answer:

Construction:

1. Draw a line segment QR = 5 cm.
2. At Q, draw QE such that ∠RQE = 30°.
3. At Q, draw QF such that ∠EQF = 90°.
4. Draw the perpendicular bisector XY to QR, which intersects QF at O and QR at G.
5. With O as centre and OQ as radius, draw a circle.
6. The major arc QKR contains the angle 30°.
7. From G, mark a point H on XY such that GH = 4.2 cm.
8. Draw a line AB through H parallel to QR. This line intersects the circle at P and P'.
9. Join QP and RP. Then ∆PQR is the required triangle.