The perimeters of two similar triangles ΔRST and ΔABC are 26 cm and 39 cm, respectively. If AB = 24 cm, then what is the length of RS?

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Given: The perimeters of similar triangles ΔRST and ΔABC are 26 cm and 39 cm, respectively. AB = 24 cm. We are to find RS.

Step 1: For similar triangles, the ratio of corresponding sides is equal to the ratio of their perimeters.

So, RS / AB = Perimeter of ΔRST / Perimeter of ΔABC

Step 2: Substitute the values:
RS / 24 = 26 / 39

Step 3: Solve for RS:
RS = 24 × (26 / 39)

Step 4: Simplify 24/39:
24/39 = 8/13

So, RS = (8/13) × 26 = (8 × 26) / 13 = 208 / 13 = 16

Therefore, RS = 16 cm.

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