You are given two rectangles with equal perimeters. The first rectangle is 12 cm long and 7 cm wide

You are given two rectangles with equal perimeters. The first rectangle is 12 cm long and 7 cm wide. The second rectangle is 5 cm wide. Find the length of the second rectangle.

From the problem statement, we know the length and width of the first rectangle, therefore we can calculate its perimeter:
P = 2 * (a + b) = 2 * (12 + 7) = 2 * 19 = 38 (cm).
The perimeters of these rectangles are equal, which means that the perimeter of the second rectangle is also 38 cm.
Knowing the perimeter and width of the second rectangle, we calculate the length of the rectangle:
38 = 2 * (a + 5),
38 = 2 * a + 10,
38 – 10 = 2 * a,
2 * a = 28,
a = 28: 2,
a = 14 (cm).
Answer: 14 cm.