Mathematics
The lengths of the sides of triangle P are 3, 4 and 5 units. Another triangle Q, which is similar to P, has one side of length 60 units, what is the smallest possible perimeter of triangle Q?
120 units
144 units
180 units
240 units
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Answer
Given,
Triangle P is similar to triangle Q
Perimeter of Triangle P = 3 + 4 + 5 = 12 units
Since the triangles are similar, the corresponding sides have a scale factor of k . One of the length of side of triangle Q is 60 units. The Corresponding scale factors will be:
Case 1 :
k = = 20
Case 2 :
k = = 15
Case 3 :
k = = 12
Among the three cases, smallest sclae factor = 12.
Smallest possible perimeter of Triangle (Q) = 12 × 12 = 144 units.
Hence, option 2 is the correct option.
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