Question

Construct a triangle with sides $5cm,6cm$ and $7cm$ and then another triangle whose sides are $\frac{7}{5}$ times of the corresponding sides of the first triangle. Write down the steps of construction.

Answer 1

Making the triangle
1) Draw a line segment AB = $5$ cm
2) Draw an arc at $6$ cm from point A. Draw an arc at $7$ cm from point B so that it intersects the previous arc
3) Joint the point of intersection from A and B.
This gives the required triangle ABC.

$\Rightarrow$ Dividing the base
4) Draw a ray AX at and acute angle from AB.
5) Plot seven points on AX; so that $A{A}_1=A_1{A}_2=A_2{A}_3=A_3{A}_4=A_4{A}_5=A_5{A}_6=A_6{A}_7$.

6) Join $A_5$ to B.
7) Draw a line from point $A_7$ parallel to $A_{5}B$ so that it joins AB' (AB extended to AB').
8) Draw a line B'C' $\parallel$ BC.
Triangle AB'C' is the required triangle