Q4 of 7 Page 239

In ΔPQR, ∠PQR = 30°, ∠PRQ = 75°, and QR = 8 cm. Let us draw a rectangle equal in area to that triangle.

Steps of Construction:


1. We draw a triangle PQR of given dimensions.



2. We draw a perpendicular bisector of side QR which intersects QR at D.


3. Join P to D.



4. Draw a line parallel to AC through B by completing the parallelogram AQBC.



5. As we have to draw a rectangle. The perpendicular bisector through D can be used.


6. The perpendicular bisector cuts parallel line through P at E.


7. From E, cut an arc of length DR on the parallel line.


8. Mark the point as F.


9. Join F to R.


10. EFRD is the required rectangle.



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