Answer :
Step 1: Draw a line segment XY = 6 cm.
Step 2: Taking X as center, draw an arc of radius 5 cm. Then, take Y as center and draw an arc of radius 4 cm. These arcs will intersect at point Z (say). Join XZ and YZ, such that XZ = 5 cm and ZY = 4 cm. Thus, ∆XYZ is the required triangle.
Step 3: Draw a ray XA making acute angle with straight line XY to the opposite side of vertex Z.
Step 4: Locate 4 points on ray XA, namely X 1 , X 2 and X 3 (since 4 is greater among 3 and 4) such that, XX 1 = X 1 X 2 = X 2 X 3 = X 3 X 4 .
Step 5: Join YX 4 and then draw a line through X 3 such that it is parallel to YX 4 and intersects on XY at Y’.
Step 6: Now draw a line through Y’ such that it is parallel to YZ and intersects on XZ at Z’.
∆XY’Z’ is the required triangle with sides 3/4 of the corresponding sides of ∆XYZ.
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