Question

Construct a triangle ABC whose sides are in the ratio 2:3:4 and perimetre 12cm. now construct triangle A'BC' similar to triangle ABC such that A'B=2/5AB. class 10 question doubt.

Answer 1

see diagram.

perimeter = 12 cm.  sides  2 x : 3x : 4x   
So x = 12/9 = 4/3 cm... Sides :   8/3 cm (AB),  4 cm (AC), 16/3 cm (BC)

Draw a line XY horizontally.  Pick a point J. From J draw arc measuring 4 (side AC) cm and cut off XY at point C.  From J draw an arc of radius 12cm (perimeter) to cut XY at D.

   Trisect DC into three parts DB, BE, EC as follows. Draw a perpendicular at D and C on the opposite sides. Draw an arc of radius 1 cm and an arc of radius 2 cm from D to cut off the perpendicular at F and G.
   
   Draw an arc of radius 1 cm and 2 cm from C to cut the perpendicular at C at H and I respectively.  Join GH and FI as shown intersecting XY at B and E respectively.

   From B draw an arc of radius BD and from C draw an arc of radius CJ to intersect at A.  Join AB and AC.