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Question

Construct a ∆ABC in which AB = 5 cm, BC = 6 cm and CA = 7 cm. Construct a triangle similar to ∆ABC, such that each of its side is 57 the corresponding sides of ∆ABC.

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Solution

Steps of Construction :

Step 1. Draw a line segment BC = 6 cm.
Step 2. With B as centre and radius equal to 5 cm, draw an arc.
Step 3. With C as centre and radius equal to 7 cm, draw another arc, cutting the previous arc at A.
Step 4. Join AB and AC.
Thus, ABC is obtained.
Step 5. Below BC, draw an acute CBX.
Step 6. Along BX, mark off seven points B1, B2, B3, B4, B5, B6, B7, such that B1B2 = B2B3 = B3B4 = B4B5 = B5B6 = B6B7.
Step 7. Join B7C.
Step 8. From B5, draw B5D B7C, meeting BC at D.
Step 9. From D, draw DECA , meeting AB at E.


Thus, EBD is the required triangle, each of whose sides is 57 the corresponding sides of ∆ABC.

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