Finding the perimeter or area of a rectengle given one or unese The length of a rectangle is 3 in longer than its width. If the perimeter of the rectangle is 46 in, find its area.

To find the area of the rectangle, we first need to determine its dimensions. Let's denote the width as \( w \). Since the length is 3 inches longer than the width, we express the length as \( l = w + 3 \). The formula for the perimeter \( P \) of a rectangle is \( P = 2l + 2w \). Plugging in the perimeter we have: \[ 46 = 2(w + 3) + 2w \] \[ 46 = 2w + 6 + 2w \] \[ 46 = 4w + 6 \] Subtracting 6 from both sides gives: \[ 40 = 4w \] Dividing by 4, we find \( w = 10 \). Now we can find the length: \[ l = w + 3 = 10 + 3 = 13 \]. Now, the area \( A \) of the rectangle is calculated as \( A = l \times w \): \[ A = 13 \times 10 = 130 \] square inches. Voila! The area of the rectangle is 130 square inches. Real-world scenarios involve areas and perimeters everywhere! Take a backyard garden: knowing the area can help you decide how much mulch to buy, while the perimeter helps in planning fencing. Or, perhaps you’re remodeling a room, and calculating the area is crucial for knowing how much flooring material to purchase. Understanding these dimensions practically can save you time, money, and help optimize your space! Solving problems like this can be tricky when starting. A common mistake is forgetting the relationships between the rectangle’s dimensions. Always double-check that the formulas and constraints fit the problem accordingly, like making sure you’ve correctly accounted for both the width and length in perimeter equations. Drawing the rectangle to visualize the problem can also make a world of difference!