Q. 24.4( 10 Votes )

Construct a triangle XYZ whose perimeter 15 cm and whose base angles are 60° and 70°.

Answer :

Here, we have been given the perimeter and base angles of the triangle.

Steps of construction are:


1. Draw a line segment using a ruler; locate points P and Q such that PQ = 15 cm.



2. Construct rays PR such that QPR = 60° and QS such that PQS = 70° using compass and then measure it with protractor.



3. Draw the bisectors PL and QM of QPR and PQS respectively. Let it intersect it at X.



4. Draw the perpendicular bisector of XP and XQ and let these intersect PQ at Y and Z respectively.


In order to draw perpendicular bisector of XP, fix one end of the compass at P at more than half of the length of XP and make a complete circle or arcs on both sides of line XP, and the other end of compass at X and intersect with the previous arcs. Do similar with the line segment XQ. Here, we’ve made complete circles.



5. Join XY and XZ.



Thus, XYZ is the required triangle.


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