The two rectangles have equal areas. The length of the first rectangle is 16 cm, and its width is 12 cm

The two rectangles have equal areas. The length of the first rectangle is 16 cm, and its width is 12 cm less than its length. The second rectangle is 32 cm long. Find the width of the second rectangle. What is the side of a square with the same area as these rectangles?

Let’s find the width of the first rectangle.
1) 16 – 12 = 4 cm – the width of the first rectangle.
Let’s calculate the area of ​​the first rectangle. Formula for the area of ​​a rectangle: S = a * b, where a is the length, b is the width of the rectangle.
2) 16 * 4 = 64 cm2 – the area of ​​the first rectangle.
Because the area of ​​the first rectangle is equal to the area of ​​the second rectangle, then we can calculate its width at a known length.
3) 64: 32 = 2 cm – the width of the second rectangle.
Now let’s answer the second question of the problem. Area of ​​a square: S = a * a or a2 (a squared), where a is the side of the square. So, with the available area equal to 64 cm2, we can find the side of the square by taking the square root of the area.
4) The square root of 64 = 8 cm is the side of the square.
Answer: 2 cm, 8 cm.