A rectangle and a square have the same area. The square has a perimeter of 32 meters and the length of the rectangle is 4 meters. What is the width of the rectangle (in meters)?

Question: A rectangle and a square have the same area. The square has a perimeter of 32 meters and the length of the rectangle is 4 meters. What is the width of the rectangle (in meters)?

Solution:
Given that,
Perimeter of square = 32 m
Area of rectangle = Area of square
And length of rectangle = 4 m

Now,
Perimeter of square,
4s = 32
⇒ s = 32/4 = 8
∴ s = 8 m
∴ Area of square = s² = 8² = 64 m²

According to the Question,
Area of rectangle = Area of square
∴ Area of rectangle = 64 m²

∴ Area of rectangle = length × width
64 = 4 × w
⇒ w = 64/4
∴ w = 16 m

So the width of the rectangle = 16 meters