To find the perimeter of the dilated triangle, we first need to determine the perimeter of the original triangle and then apply the scale factor.
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Calculate the perimeter of the original triangle: \[ \text{Perimeter} = \text{leg}_1 + \text{leg}_2 + \text{hypotenuse} \] Substituting the given lengths: \[ \text{Perimeter} = 24 , \text{cm} + 7 , \text{cm} + 25 , \text{cm} = 56 , \text{cm} \]
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Apply the scale factor of \( \frac{1}{4} \) to find the perimeter of the dilated triangle: \[ \text{Perimeter of dilated triangle} = \text{Perimeter of original triangle} \times \frac{1}{4} \] Substituting the perimeter we calculated: \[ \text{Perimeter of dilated triangle} = 56 , \text{cm} \times \frac{1}{4} = 14 , \text{cm} \]
Therefore, the perimeter of the dilated triangle is 14 cm.