The length of a rectangle is 5 ft longer than its width. If the perimeter of the rectangle is 46 ft , find its area

Let's start solving this problem! First, denote the width of the rectangle as \( w \). Then, since the length is 5 ft longer than the width, we can express the length as \( w + 5 \). The formula for the perimeter \( P \) of a rectangle is given by: \[ P = 2 \times (\text{length} + \text{width}) \] Plugging in the values we have: \[ 46 = 2 \times ((w + 5) + w) \] Simplifying that gives us: \[ 46 = 2 \times (2w + 5) \\ 46 = 4w + 10 \] Now, subtract 10 from both sides: \[ 36 = 4w \] Dividing both sides by 4 yields: \[ w = 9 \text{ ft} \] Now to find the length: \[ \text{Length} = w + 5 = 9 + 5 = 14 \text{ ft} \] Now, to find the area \( A \) of the rectangle, we use the formula: \[ A = \text{length} \times \text{width} = 14 \times 9 = 126 \text{ square feet} \] So, the area of the rectangle is 126 square feet! Now, let's explore this rectangle further, shall we? The discovery of rectangles spans back to the ancient civilizations, where they learned about these shapes through practical applications, like land measurement and construction. The Pythagorean theorem was even used to create rectangular plots, showcasing geometry's importance in daily life! Rectangles surround us in daily life, making them not just a math problem but a reality. From the dimensions of a door frame to the layout of a room, understanding rectangles helps us design functional spaces effectively. The concepts of perimeter and area allow architects and interior designers to get the most out of their layouts. How cool is that?