Final answer:
To find the lengths of the sides of a similar triangle with a perimeter of 26cm, divide the perimeter of the original triangle by the perimeter of the similar triangle to find the scale factor. Multiply each length of the original triangle by the scale factor to find the lengths of the sides of the similar triangle.
Step-by-step explanation:
To find the lengths of the sides of a similar triangle with a perimeter of 26cm, we need to find the scale factor between the original triangle and the similar triangle. The scale factor can be found by dividing the perimeter of the original triangle by the perimeter of the similar triangle. In this case, the perimeter of the original triangle is 15cm + 20cm + 30cm = 65cm. So, the scale factor is 65cm / 26cm = 5/2.
Now we can use the scale factor to find the lengths of the sides of the similar triangle. The lengths of the sides of the original triangle are 15cm, 20cm, and 30cm. To find the corresponding lengths of the sides in the similar triangle, we multiply each length by the scale factor. So, the lengths of the sides of the similar triangle are (15cm * 5/2), (20cm * 5/2), and (30cm * 5/2).
Simplifying, we get: ED = 6cm, DF = 8cm, EF = 12cm.