Question

Construct a triangle ABC, whose perimeter is 13.5 cm and whose base angles are 60° and 75°.

Answer 1

The steps given below need to be followed to construct the required triangle

Step I: Draw a line segment PQ of 13.5 cm length (AB + BC + CA = 13.5 cm)

Step II: Construct ∠RPQ measuring 60° at point P and ∠PQS measuring 75° at point Q.

Step III: Bisect ∠RPQ and ∠PQS. Let these bisectors intersect each other at point A.

Step IV: Draw perpendicular bisectors UV of AP and WX of QA.

Step V: Let UV intersect PQ at B and WX intersect PQ at C. Join AB and AC.

ΔABC is the required triangle.