Two rectangular picture frames are similar in shape. A corresponding pair of sides are of length 50 cm and 75 cm. The other side length on the smaller frame is 70 cm. Find the perimeter of the larger frame.
Let the length of the other side on the larger frame be x cm.
Since the frames are similar in shape, the ratios of corresponding sides are equal.
Therefore, we can set up the following proportion:
\(\frac{50}{x} = \frac{70}{75}\)
Solving for x, we get:
\(x = \frac{50 \cdot 75}{70} = 53.57\)
So, the length of the other side on the larger frame is approximately 53.57 cm.
The perimeter of the larger frame is:
\(2(50 + 75 + 53.57) = 2(178.57) = \boxed{357.14}\) cm.