Answer:
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 = [tex]x[/tex]
Therefore, the area of a square = [tex]x \times x = x^2[/tex]
If the square has the same area as the rectangle, then
[tex]x^2=16[/tex]
Square root both sides: [tex]x = \sqrt{16} =\pm4[/tex]
Since the length of a side cannot be negative, [tex]x=4[/tex] 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 = [tex]x[/tex]
Perimeter of a square = 4 x [tex]x[/tex] = 4[tex]x[/tex]
If a square has the same perimeter as the rectangle, then
[tex]4x=20[/tex]
Divide both sides by 4: [tex]x=20 \div 4 = 5[/tex]
side length of this square = 5 cm
