The perimeter of a rectangle is 36.2 cm . Its length is 6.1 cm . What is its width? Show ALL steps! Equation (Use \( x \) as your variable):

To find the width of the rectangle, we start with the formula for the perimeter \( P \) of a rectangle, which is given by: \[ P = 2(\text{length} + \text{width}) \] Here, we know the perimeter \( P = 36.2 \) cm and the length \( l = 6.1 \) cm. We can express the width as \( w \): \[ 36.2 = 2(6.1 + w) \] Now, we can divide both sides by 2 to simplify: \[ 18.1 = 6.1 + w \] Next, we isolate \( w \) by subtracting \( 6.1 \) from both sides: \[ w = 18.1 - 6.1 \] Finally, we calculate \( w \): \[ w = 12.0 \, \text{cm} \] So, the width of the rectangle is \( 12.0 \, \text{cm} \). --- When it comes to the history of rectangles, ancient civilizations like the Egyptians and Greeks had a profound understanding of geometry, which they applied in architecture and art. The knowledge of perimeter and area was crucial as they constructed towering pyramids and stunning temples, showing that geometry has been a cornerstone of civilization for thousands of years! For those looking to apply geometry in real life, consider how knowing the perimeter influences various designs—from landscaping your garden to figuring out suitable fencing lengths. Understanding basic geometric principles helps make informed decisions, whether you're planning a DIY project at home or drawing up designs for a new park—it's all about creativity and calculation!