To construct a triangle similar to ΔABC in which BC = 4. 5 cm, ∠B = 45° and ∠C = 60°, using a scale factor of 3/7, BC will be divided in the ratio
(a) 3 : 4 (b) 4:7
(c) 3 : 10 (d) 3 : 7
Steps of Construction:
1. First we construct the triangle ABC with the given dimensions.
2. Draw a line segment BC of length 4. 5 cm. Make an angle of 45° from B and an angle 60° from C.
3. The point where the rays meet is A.
4. Now draw a ray making an acute angle with BC. Make 7 equal arcs.
5. Join the last arc cut point with C and from 3rd arc, cut point draw a line parallel to B7C cutting BC at C’.
6. From C’ draw a line parallel to AC cutting AB at A’.
A’BC’ is or required triangle.
7. Now we see that our line BC gets divided into the ratio of 3:4.
So (a) 3:4 is the answer.