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