Finding the perimeter or area of a rectange gength of a rectangle is four times its width. The le area of the rectangle is \( 400 \mathrm{~m}^{2} \), find its perimeter.

Let's break it down! If the width of the rectangle is \( w \), then length \( l \) can be expressed as \( l = 4w \). The area of the rectangle is given by the formula \( A = l \times w \). So, substituting the length, we have: \[ 400 = 4w \times w \implies 400 = 4w^2 \implies w^2 = 100 \implies w = 10 \, \text{m} \] Using \( w \) to find length: \[ l = 4 \times 10 = 40 \, \text{m} \] Now, the perimeter \( P \) is calculated with the formula \( P = 2(l + w) \): \[ P = 2(40 + 10) = 2 \times 50 = 100 \, \text{m} \] So, the perimeter of the rectangle is \( 100 \, \text{m} \)! Now, let’s keep the fun going! If you think rectangles can only be basic shapes, surprise! They’re like the superheroes of geometry, helping us understand everything from floor plans to picture frames. Every rectangular area you see has an invisible perimeter wrapping it up tightly. For the mathematically curious, exploring the world of rectangles can lead to some fascinating concepts like the Golden Ratio! While rectangles are straightforward, try encountering golden rectangles—these can be linked to aesthetics and nature. It’s geometry’s way of making the mundane look marvelous!