The two rectangles have the same area. The length of the first is 16cm, the second is 12m.

The two rectangles have the same area. The length of the first is 16cm, the second is 12m. But the perimeter of the first rectangle, if the perimeter of the second is 32cm.

By the condition of the problem, we know the perimeter of the second rectangle, which is 32 cm. By dividing this perimeter in half, we will find the sum of the length and width of the second rectangle.

So, let’s find the sum of the length and width of the second rectangle:

32: 2 = 16 (cm).

Also, from the condition, we know that the length of the second rectangle is 12 cm.

Find the width of the second rectangle by subtracting the length of the second rectangle from the found sum of the length and width. So, we get the expression:

16 – 12 = 4 (cm).

Now we can calculate the area of ​​the second rectangle, since we know the lengths of its two sides:

S = 12 * 4 = 48 (cm²).

The area of ​​the second rectangle is equal to the area of ​​the first rectangle, respectively, the area of ​​the first rectangle is also 48 cm².

Now we need to find the width of the first rectangle by dividing the already found area by its length, which, according to the condition of the problem, is 16 m:

48: 16 = 3 (cm).

Now we also know the lengths of the two sides of the first rectangle. Let’s find its perimeter if its length is 16 cm and width is 3 cm:

P = 2 (16 + 3) = 2 * 19 = 38 (cm).
Answer: The perimeter of the first rectangle is 38 cm.