Question : The perimeter of two similar triangles is 30 cm and 20 cm, respectively. If one side of the first triangle is 9 cm. Determine the corresponding side of the second triangle.
Option 1: 13.5 cm
Option 2: 6 cm
Option 3: 15 cm
Option 4: 5 cm
Correct Answer: 6 cm
Solution :
Let $\triangle$ABC and $\triangle$DEF be two similar triangles of perimeters P
1
and P
2
, respectively.
Also, let AB = 9 cm, P
1
= 30 cm and P
2
= 20 cm
Then, $\frac{AB}{DE}=\frac{BC}{EF}=\frac{AC}{DF}=\frac{P_{1}}{P_{2}}$ [Ratio of corresponding sides of similar triangles is equal to the ratio of their perimeters.]
⇒ $\frac{AB}{DE}=\frac{P_{1}}{P_{2}}$
⇒ $\frac{9}{DE}=\frac{30}{20}$
⇒ DE = $\frac{9 \times 20}{30} = 6$ cm
$\therefore$ The corresponding side of the second triangle is 6 cm.
Hence, the correct answer is 6 cm.
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