To find the perimeter of the dilated triangle, we first need to calculate the perimeter of the original triangle with side lengths of 6 cm, 6 cm, and 5 cm.
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Calculate the perimeter of the original triangle: \[ \text{Perimeter} = 6 + 6 + 5 = 17 \text{ cm} \]
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When the triangle is dilated with a scale factor of 4, each side length is multiplied by the scale factor: \[ \text{New side lengths} = 4 \times 6 = 24 \text{ cm}, \quad 4 \times 6 = 24 \text{ cm}, \quad 4 \times 5 = 20 \text{ cm} \]
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Calculate the perimeter of the dilated triangle: \[ \text{Perimeter of dilated triangle} = 24 + 24 + 20 = 68 \text{ cm} \]
Therefore, the perimeter of the dilated triangle is 68 cm.