The length of a rectangle is 5 m longer than its width. If the perimeter of the rectangle is 46 m , find its area. \[ 1 \mathrm{~m} \]

To solve for the area of the rectangle, we start with the formulas for perimeter and area. The perimeter \( P \) of a rectangle is given by: \[ P = 2(\text{length} + \text{width}) \] Given that the length \( L \) is 5 m longer than the width \( W \), we can express this as: \[ L = W + 5 \] Now substituting this into the perimeter equation gives us: \[ 46 = 2((W + 5) + W) \] \[ 46 = 2(2W + 5) \] \[ 46 = 4W + 10 \] \[ 36 = 4W \] \[ W = 9 \, \text{m} \] Now that we have the width, we can find the length: \[ L = W + 5 = 9 + 5 = 14 \, \text{m} \] The area \( A \) of the rectangle is given by: \[ A = \text{length} \times \text{width} = L \times W = 14 \times 9 = 126 \, \text{m}^2 \] So, the area of the rectangle is \( 126 \, \text{m}^2 \). Now let’s have some fun with this! Did you know that rectangles of different sizes can hold the same area? Just like how you can rearrange furniture in your living room! A rectangle that is 14 m by 9 m can be visually transformed into a taller and slimmer version. Keep in mind, though, that while they may hold the same space, the perimeter can vary based on those dimensions! If you’re ever stuck on problems like this, it can help to sketch it out or even use a piece of graph paper. Drawing out rectangles can make it easier to visualize how changing one dimension affects the others. And always remember to check your equations—those pesky negative signs can sneak in and change everything!