Construct an isosceles triangle whose base is 8 cm and altitude 4 cm and then another triangle whose sides are times the corresponding sides of the isosceles triangle.

Question

Philoid · Accepted Answer

Steps of Construction:

1. Draw a line segment BC of length 8cm.

2. Now as we know that the altitude of the isosceles triangle is also the bisector of the baseline. So we draw a perpendicular bisector of line BC.

3. We cut an arc of length 4cm( length of altitude). The arc cut point is A.

4. Join AB and AC.

5. Now we have draw a triangle which is 3/2 times of this triangle that a triangle which is bigger than this.

6. So we extend BC along C and BA along A as in figure.

7. Draw a ray BZ making an acute angle with BC. Make 3 equal arcs along BZ.

7. Join the second arc with C. Now draw a line from last arc cut point parallel to the previous line cutting the extended BC at C’.

8. From C’ draw another line parallel to CA cutting the extended BY at A’.

9. A’BC’ is our required triangle.