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
✓
Answer
Analysis: $\triangle ABC \sim \triangle LMN$
$\therefore \frac{ AB }{ LM }=\frac{ BC }{ MN }=\frac{ AC }{ LN } \ldots . . .[$ Corresponding sides of similar triangles]
$\therefore \frac{5}{ LM }=\frac{5}{ MN }=\frac{5}{ LN }=\frac{6}{7} \quad \ldots .$. [Given]
$\therefore \frac{5}{ LM }=\frac{6}{7}$
$\therefore L M=\frac{5 \times 7}{6}$
$\therefore LM =5.8 cm$ (approx)
$\therefore L M=M N=L N=5.8 cm$ (approx) $\quad \ldots .$. [Equilateral triangle]
Steps of Construction:
| /_\ABC | /_\PQR | |
| i. | Draw seg BC of 5cm | Draw seg MN of 5.8 cm |
| ii. | Draw two arcs at 5cm from point B and point Cspectively. | Draw two arcs at 5.8 cm from point M and point 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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