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

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

First, find the width of the second rectangle. We know that the perimeter is 32 and the length is 12 cm, which means:
(32 – 12 – 12) ÷ 2 = 4 cm
That is, the width is 4 cm.
Next, we find the area of the second rectangle. The area is equal to the product of the sides of the rectangle.
S = 4 × 12 = 48 cm2.
Since the areas of the two rectangles are equal, it means that the area of the first is 48 cm2. Find the width of the second rectangle.
48 ÷ 16 = 3 cm
This means that the width of the first rectangle is 3 cm.
We find the perimeter.
P = (16 + 3) × 2 = 38 cm.
Answer: The perimeter is 38 cm.

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