Final answer:
To find the perimeter of triangle ABC, subtract the given BC-AD value from the given BD value to find AD, and then calculate AB, BC, and AC by adding the appropriate values. Finally, sum up the lengths of all three sides to find the perimeter.
Step-by-step explanation:
To find the perimeter of triangle ABC, we need to determine the lengths of all three sides of the triangle. We know the perimeter of triangle ABD is 30 cm, and BC-AD=2 cm. Given that BD=5 cm, we can find the length of AD by subtracting 2 cm from BD, which gives us AD=5 cm - 2 cm = 3 cm.
Now that we have the lengths of all three sides (AB=AD+BD=3 cm+5 cm=8 cm, BC=AD+DC=3 cm+2 cm=5 cm, and AC=AB+BC=8 cm+5 cm=13 cm), we can calculate the perimeter as AB+BC+AC=8 cm+5 cm+13 cm= 26 cm.
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