Question

Construct an isosceles triangle whose base is 3.2 cm and altitude 1.7 cm and then construct another triangle whose sides are 1 1/2 times the corresponding sides of the isosceles triangle.

Answer 1

Step1: Draw the base of triangle AB = 3.2 cm

Step2: Using scale mark the centre of AB as M and from M using protractor draw a line perpendicular to AB

Step3: Take distance 1.7 cm in compass keep the needle of the compass on point M and mark an arc intersecting ray drawn in step2. Mark the intersection point as C and join AC and BC.

Step4: Draw a ray at any angle below AB from A

Step5: Take any distance in compass and keeping the needle of the compass on point A cut an arc on ray constructed in step4 and name that point X₁. Keeping the distance in compass same keep the needle of the compass on point X₁ and cut an arc on the same ray and mark that point as X₂. Draw 3 such parts (greater of 3 and 2 in 3/2), i.e. by repeating this process mark points upto X₃

Step6: Join X₂ and B (2 being smaller of 3 and 2 in 3/2 and not X₃ because the ratio 3/2 is greater than 1)

Step7: Now extend AB and draw a line parallel to X₂B from X₃ intersecting AB at D

Step8: Extend AC and draw a line parallel to BC from point D intersecting AC at E and ΔADE whose sides are 3/2 i.e. 1 1/2 times ΔABC is ready