Question

Construct a right-angled triangle whose perimeter is equal to 10 cm and one acute angle equal to ${60}^{\circ }$.

Answer 1

Steps of construction :

(i) Draw a line segment PQ = 10 cm.

(ii) At P, draw a ray PX making an angle of ${90}^{\circ }$ and at Q, QY making an angle of ${60}^{\circ }$.

(iii) Draw the angle bisector of $\angle Pand\angle Q$ meeting each other at A.

(iv) Draw the perpendicular bisectors of AP and AQ intersecting PQ at B and C respectively.

(v) Join AB and AC.

$△$ABC is the required triangle.