Q. 34.8( 6 Votes )

# Construct triangle PQR in which PQ + PR = 6.5 cm, QR = 5.4cm, ∠Q = 40°.

Answer :

We have been given one of the side of triangle and the sum of the other two sides along with one of the angle of a triangle.

Steps of construction:

1. Draw a line segment XY large enough with the use of a ruler.

2. Locate points Q and R on XY, such that QR = 5.4 cm using a ruler.

3. Draw a line segment QZ sufficiently large such that ∠RQZ = 40°; do this with the help of a protractor.

4. From the segment QZ, cut off the line segment QD such that QD = 6.5 cm (here, we have presumed PQ + PR = QD), using a compass and a ruler.

With Q as centre, set the compass at 6.5 cm length and draw a circle or semicircle or an arc, and name the point where it intersects at QZ as D.

5. Join DR.

6. Draw perpendicular bisector of DR and let it meet QR at P. For perpendicular bisector of DR, fix the compass at a length just more than the length of DR and draw circles or arcs on both sides of the line segment DR taking D and R as centres one by one.

7. Join PR.

Thus, PQR is the required triangle.

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