To find the perimeter of the dilated triangle, we first need to calculate the perimeter of the original triangle and then apply the scale factor.
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Calculate the perimeter of the original triangle: The sides of the original triangle are 25 cm, 7 cm, and 24 cm.
\[ \text{Perimeter} = 25 , \text{cm} + 7 , \text{cm} + 24 , \text{cm} = 56 , \text{cm} \]
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Dilate the perimeter by the scale factor of 14: The perimeter of the dilated triangle can be found by multiplying the original perimeter by the scale factor.
\[ \text{Dilated Perimeter} = 56 , \text{cm} \times 14 = 784 , \text{cm} \]
So, the perimeter of the dilated triangle is 784 cm.