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a) 4 cm

b) 5 cm

Step-by-step explanation:

a) Area of a rectangle = width x length

From inspection, the width of this rectangle is 2 cm and the length is 8 cm

⇒ area of the rectangle = 2 x 8 = 16 cm²

A square has 4 sides of equal measure.

Let the side of a square =

Therefore, the area of a square =

If the square has the same area as the rectangle, then

Square root both sides:  

Since the length of a side cannot be negative, only

So the side length of the square = 4 cm

b) Perimeter of a rectangle = 2 x length + 2 x width

⇒ perimeter of the rectangle = (2 x 8) + (2 x 2) = 20 cm

Since the side lengths of a square are equal, and a side length =

Perimeter of a square = 4 x = 4

If a square has the same perimeter as the rectangle, then

Divide both sides by 4:  

side length of this square = 5 cm

a)4cm  b)5cm

Step-by-step explanation:

a)

Area of the rectangle is 16cm².

When,

Area of the rectangle is equal to the area of the square then,

Area of square=16cm²

Now,

→Length=√Area

→Length=√16cm²

→Length=4cm

b)

The perimeter of rectangle=20cm

When,

The perimeter of the rectangle is equal to the perimeter of the square then,

The perimeter of square=20cm

Now,

Length=Perimeter/4

Length=20cm/4

Length=5cm