Draw a right triangle in which the sides (other than hypotenuse) are of lengths 5cm and 4cm. Then construct another triangle whose sides are 5/3 times the corresponding sides of the given triangle.
Draw a right triangle in which the sides (other than hypotenuse) are of lengths 5cm and 4cm. Then construct another triangle whose sides are 5/3 times the corresponding sides of the given triangle.

Steps of construction:

1. Mark a line segment BC=5cm with the help of ruler.

2. At B, draw perpendicular BX and cut off BA=4cm.

3. Then, join AC. Then, ABC is the triangle

4. Draw a ray BY making an acute angle with BC and cut off 5 equal parts making B{{B}_{1}}={{B}_{1}}{{B}_{2}}={{B}_{2}}{{B}_{3}}={{B}_{3}}{{B}_{4}}={{B}_{4}}{{B}_{5}}

5. Now, join {{B}_{3}} and C.

6. From {{B}_{5}}, draw {{B}_{5}}C' parallel to {{B}_{3}}C and C’A’ parallel to CA.

Then, \vartriangle A'BC'is the required triangle.