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Question
Construct an equilateral ∆ABC with side 5 cm. ∆ABC ~ ∆LMN, ratio the corresponding sides of triangle is 6 : 7, then construct ΔLMN and ΔABC.
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Solution
Analysis:
∆ABC ∼ ∆LMN
∴ `(AB)/(LM) = (BC)/(MN) = (AC)/(LN)` ...[Corresponding sides of similar triangles]
∴ `5/(LM) = 5/(MN) = 5/(LN) = 6/7` ...[Given]
∴ `5/(LM) = 6/7`
∴ `LM = (5 xx 7)/6`
∴ LM = 5.8 cm (approx)
∴ LM = MN = LN = 5.8 cm (approx) ...[Equilateral triangle]
Steps of Construction:
| ∆ABC | ∆LMN | |
| i. | Draw seg BC of 5 cm | Draw seg MN of 5.8 cm |
| ii. | Draw two arcs at 5 cm from point B and point C respectively. | Draw two arcs at 5.8 cm from point M and point N respectively. |
| iii. | Name the point of intersection of two arcs as A. | Name the point of intersection of two arcs as L. |
| iv. | Join seg AB and seg AC. | Join seg LM and seg LN. |
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