Question

Construct a triangle $ABC$, whose perimeter is $12cm$ and whose sides are in the ratio $2:3:4$.

Answer 1

Steps of construction
$1$. Draw a line segment and locate points $X,Y$ such that $XY=12cm$.
$2$. Draw a ray $XZ$, making an acute angle with $XY$ and drawn in the down-ward direction.
$3$. From $X$, locate $(2+3+4)=9$ points at equal distances along $XZ$.
$4$. Mark point $L,M,N$ on $XZ$ such that $XL=2$ parts, $LM=3$ parts and $MN=4$ parts.
$5$. Join $NY$. Through $L$ and $M$, draw $LB\parallel NY$ and $MC\parallel NY$, intersecting $XY$ in $B$ and $C$ respectively.
$6$. With $B$ as center and $BX$ as radius, draw an arc; with $C$ as a centre and $CY$ as radius, draw an arc cutting the previous arc at $A$.
$7$. Join $AB$ and $AC$.
Then $ABC$ is the required triangle.