Question

Construct a triangle PQR with PQ = 5.4 cm, QR = 4.6 cm and ∠Q = 60°. Draw the perpendicular PS at QR, measure the lengths of SP and SQ,

Answer 1

Steps:
1. Draw PQ = 5.4 cm.
2. At P, construct ∠PQT = 60°.
3. With Q as centre and radius 4.6 cm, draw an arc intersecting ray QT at R.
4. Join PR.
Thus, PQR is the required triangle.
Draw PU, the perpendicular bisector of QR intersecting QR at S.
Then, we have
SQ = 2.3 cm and SP = 4.8 cm