The area of a square with a side of 5/9 dm is equal to the area of a rectangle whose width is 2 1/2 dm

The area of a square with a side of 5/9 dm is equal to the area of a rectangle whose width is 2 1/2 dm. What is the length of the rectangle and its perimeter?

We find the area of a square using the formula:
S sq. = a² = (5/9) = 25/81 (dm²).
S sq. = S straight. = 25/81 (dm²).
We write down the formula for the area of a rectangle, from which we find the length:
S straight. = a * b → a = S straight. / b.
a = 25/81 / 5/2 = 25/81 * 2/5 = 10/81 (cm) – the length of the rectangle.
Find the perimeter of the rectangle:
P is straight. = 2 * (a + b) = 2 * (5/2 + 10/81) = 2 * 425/162 = 425/81 = 5 20/81 (cm).
Answer: the length of the rectangle is 10/81 cm, the perimeter is 5 20/81 cm.