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.
To find the perimeter of the larger frame, we need to first determine the length of the corresponding side on the larger frame.
Since the two frames are similar in shape, the ratio of the corresponding sides will be the same. Therefore, we can set up a proportion to find the missing side length on the larger frame:
\( \frac{50}{70} = \frac{75}{x} \)
Cross multiplying, we get:
\( 50x = 70 \times 75 \)
\( 50x = 5250 \)
\( x = \frac{5250}{50} \)
\( x = 105 \)
So, the missing side length on the larger frame is 105 cm.
Now we can find the perimeter of the larger frame:
Perimeter = 2(50 + 75 + 105) = 2(230) = 460 cm
Therefore, the perimeter of the larger frame is 460 cm.