Question

Construct a triangle with sides 5 cm , 5.5 cm and 6.5 cm. Construct another triangle whose sides are $\frac{3}{5}$ times the corresponding sides of the first triangle.

Answer 1

Steps of construction :

1. Construct $\Delta$ ABC with given lengths of sides.

2. Below BC, make an acute angle $\angle$ CBX

3. Along BX, mark off five points $B_1,B_2,B_3,B_4$ and $B_5$ such that $B{B}_1=B_1{B}_2=B_2{B}_3=B_3{B}_4=B_4{B}_5$

4. Join $B_{5}C$

5. From $B_3$ draw $B_{3}D\parallel B_{5}C$ (by making an angle $\angle B{B}_{3}D$ = $\angle B{B}_{5}C$), meeting BC at D.

6. From D, draw $DE\parallel CA$ by making an angle ($\angle$ BDE = $\angle$ BCA), meeting AB at E.

7.$\Delta$ EBD is the required triangle, each of whose sides is $\frac{3}{5}$ of hte corresponding side of $\Delta$ ABC