Question

Construct `trianglePQR` in which QR=3.2 cm, PQ+PR=5.9 cm and `angleR-angleQ=60^(@)`

Answer 1

Step 1: Draw line segment QR = 3.2 cm.
Step 2: Draw `bar(RX)`, such that `angleQRX = (90^(@)+(angleR-angleQ)/(2))=90^(@)+30^(@)=120^(@)`.
Step 3: Taking Q as the center and a radius equal to 5.9 cm (PQ + PR), draw an arc intersecting `bar(RX)` at S.
Step 4: Draw RY, such that
`angleQRY=(angleR-angleQ)/(2) = 30^(@)`, intersecting QS at T.
Step 6: Draw the perpendicular bisector of `bar(RT)` intersecting `bar(QS)` at P.
Step 7: Join P and R. PQR is the required triangle.