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.

Rate this question :

Construct an equilateral triangle of height 4.3 cm.

Karnataka Board - Mathematics Part IIConstruct an isosceles triangle whose altitude is 5 cm and whose vertex angle is 70 °.

Karnataka Board - Mathematics Part IIConstruct a triangle MNP in which MN = 4.5 cm, MP = 5.2 cm and length of perpendicular from M on NP is 3.8 cm.

Karnataka Board - Mathematics Part IIConstruct an equilateral triangle of height 5.2 cm. Measure approximate length of the its side.

Karnataka Board - Mathematics Part IIConstruct a triangle ABC in which BC = 3.4 cm AB – AC = 1.5 cm and ∠B = 45°.

Karnataka Board - Mathematics Part IIConstruct an isosceles triangle whose altitude is 5 cm and whose vertex angle is 80°.

Karnataka Board - Mathematics Part IIConstruct a triangle ABC in which AB + AC = 5.6 cm, BC = 4.5cm and ∠B = 45°.

Karnataka Board - Mathematics Part IIConstruct a triangle PQR in which PQ = 5.5 cm, PR = 6.2 cm and length of the perpendicular from P on QR is 4 cm.

Karnataka Board - Mathematics Part IIConstruct a triangle PQR in which PQ = 4 cm, QR = 4.5 cm and ∠Q = 60°.

Karnataka Board - Mathematics Part IIConstruct a triangle XYZ whose perimeter 15 cm and whose base angles are 60° and 70°.

Karnataka Board - Mathematics Part II