Question

Construct a triangle $ABC$ in which $AB=5.8cm,BC+CA=8.4cm$ and $\angle B={60}^{\circ }$

Answer 1

Steps of construction

$1$. Draw a line segment $AB$ of length $5.8cm$.

$2$. Draw a line segment $BX$, sufficiently large such that $\angle ABX={60}^{\circ }$.

$3$. From the segment $BX$, cut off line segment $BD$ of length $8.4cm$.

$4$. Join $AD$.

$5$. Draw the perpendicular bisector of $AD$ and let it meet $BD$ at $C$.

$6$. Join $AC$.

Then $ABC$ is the required triangle.