Construct a in which AB = 5 cm. altitude CD = 3 cm. Construct a similar to such that side of is 1.5 times that of the corresponding sides of .

The steps involved in the required construction are:

1) Draw a line segment AB= 5 cm. Using a protractor, draw ∠ABE=60°. Keeping A as the center, draw a circle of any radius, intersecting extended AB at F and G.

2) Keeping F as the center and any radius draw a circular arc. Now, Keeping G as the center and same radius as before, draw another arc, intersecting previous arc at H. Join and extend AH. Keeping A as the center and radius 3 cm, draw an arc, intersecting extended AH at I.

3) Keeping I as the center, draw a circle of any radius, intersecting extended AH at J and K. Keeping J as the center and any radius draw a circular arc. Now, Keeping K as the center and same radius as before, draw another arc, intersecting previous arc at L. Join and extend IL, intersecting BE at C. Join AC.

4) Draw any line segment AM, making an acute angle with AB and opposite to the vertex C. Taking A as the center and any radius, draw an arc, intersecting AM at N. Taking N as the center and radius AN, draw an arc, intersecting AM at O. Taking O as the center and radius AN, draw an arc, intersecting AM at P. Join BO.

5) Taking O as the center and any radius, draw an arc., intersecting AM and BO at Q and R respectively. Taking P as the center and radius OQ, draw an arc, intersecting AM at S. Taking S as the center and radius QR, draw an arc, intersecting previous arc at T. Join and extend PT, intersecting extended AB at U.

6) Taking B as the center and any radius, draw an arc., intersecting BA and BC at W and X respectively. Taking U as the center and radius BW, draw an arc., intersecting AU at Y. Taking Y as the center and radius WX, draw an arc, intersecting previous arc at Z. Join and extend UZ, intersecting extended AC at V.

7) ∆AUV is the required triangle.