Construct a ΔABC in which BC = 5 cm, ∠C = 60° and altitude from A equal to 3 cm. Construct a ΔADE similar to ΔABC such that each side of ΔADE is 3/2 times the corresponding side of ΔABC. Write the steps of construction.
Steps of Construction:
1. First we have to draw triangle of the given dimensions.
2. Draw a line l.
3. Take any point S on this line, and draw an angle of 90° from this point.
4. From S, draw an arc of length 3cm(length of altitude) cutting the perpendicular at A.
5. From A draw an angle of 30°, which cuts line l at C.
6. From C, draw an arc of length 5cm( length of BC) cutting line l at B.
7. Join AB. Then ABC is the triangle of given dimensions.
8. Draw a ray AP making an acute angle with the line AB.
9. As we have to make a triangle ADE which is 3/2 times of this triangle, i. e. a bigger triangle. We extend AB to Y and AC to Z.
10. With A as center draw an arc on the ray AP. Then A1 as center and same radius draw another arc till we get A3.
11. Join A2B.
12. From A3 draw a line parallel to A2B cutting the AY at D.
13. From D, draw a line parallel to BC, cutting AZ at E.
14. Then ADE is the required triangle.