Question : $\triangle$ABC is similar to $\triangle$PQR. If the ratio of the perimeter of $\triangle$ABC and the perimeter of $\triangle$PQR is 24 : 16 and PQ = 4.8 cm, then the length (in cm) of AB is:
Option 1: 8.6
Option 2: 7.2
Option 3: 4.6
Option 4: 2.8
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Correct Answer: 7.2
Solution :
Given: $\triangle$ABC is similar to $\triangle$PQR.
The ratio of the perimeter of $\triangle$ABC and the perimeter of $\triangle$PQR is 24 : 16 and PQ = 4.8 cm.
Since, $\triangle$ABC is similar to $\triangle$PQR,
We know,
The ratio of similar sides of the two similar triangles = The ratio of their perimeter
So, AB : PQ = 24 : 16
⇒ AB = $\frac{24}{16}$ × PQ = $\frac{24}{16}×4.8 = 7.2$ cm
Hence, the correct answer is 7.2.
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