Question

Construct a triangle of sides $4.2cm,5.1cm$ and $6cm$. Then construct a triangle similar to it, whose sides are $\frac{2}{3}$ of corresponding sides of the first triangle.

Answer 1

Draw a line segment $AB=4.2cm$
Draw an arc at $5.1cm$ from point $A$.
Draw an arc at $6cm$ from point $B$ so that it intersects the previous arc.
Joint the point of intersection from $A$ and $B$.
This gives the required $△ABC$.

Dividing the base in $2:3$ ratio:

Draw a ray $AX$ at an acute angle from $AB$.
Plot three points on $AX$ so that; $A{A}_1=A_1{A}_2=A_2{A}_3$
Join $A_3$ to $B$.
Draw a line from point $A_2$ so that this line is parallel to $A_{3}B$ and intersects $AB$ at point $B^{\prime }$.
Draw a line from point $B^{\prime }$ parallel to $BC$ so that this line intersects $AC$ at point $C^{\prime }$.