NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 6: Triangles - Exercise 6.3

Question 7

Step 1: Since \(\triangle ABC \sim \triangle DEF\), their corresponding sides are in the same ratio (scale factor).

Step 2: The sides \(AB\) and \(DE\) correspond to each other. So, scale factor \(k = \dfrac{AB}{DE} = \dfrac{4}{6} = \dfrac{2}{3}\).

Step 3: Now use this scale factor to find the other sides of \(\triangle ABC\):

• \(BC\) corresponds to \(EF\). So, \(BC = EF \times k = 9 \times \dfrac{2}{3} = 6\,\text{cm}\).
• \(CA\) corresponds to \(FD\). So, \(CA = FD \times k = 12 \times \dfrac{2}{3} = 8\,\text{cm}\).

Step 4: Now we know all three sides of \(\triangle ABC\): \(AB = 4\,\text{cm}, BC = 6\,\text{cm}, CA = 8\,\text{cm}.\)

Step 5: Perimeter means the sum of all three sides: \(\text{Perimeter} = AB + BC + CA = 4 + 6 + 8 = 18\,\text{cm}.\)