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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