SUBMIT ANSWER [-/2 Points] DETAILS MY NOTES KAUFACS10 2.4.047. Solve the problem by setting up and solving an appropriate algebraic equation. Suppose that the length of a certain rectangle is 6 meters less than four times its width. The perimeter of the rectangle is 78 meters. Find the length and width of the rectangle. length \( \square \) m width \( \square \) m Additional Materials eBook SUBMIT ANSWER -/1 Points] DETAILS MY NOTES

To solve this problem, let's start by defining the width of the rectangle as \( w \) meters. According to the information provided, the length \( l \) can be expressed as \( l = 4w - 6 \). The formula for the perimeter \( P \) of a rectangle is given by \( P = 2l + 2w \). Setting this equal to 78 meters, we get the equation \( 2(4w - 6) + 2w = 78 \). Simplifying gives us \( 10w - 12 = 78 \), leading us to the solution \( w = 9 \) meters. Substituting \( w \) back, we find \( l = 4(9) - 6 = 30 \) meters. So, the length is 30 meters, and the width is 9 meters! If you enjoyed this algebraic adventure, consider exploring the fascinating world of geometry, where you can learn how the shapes around us are constructed and their properties. Geometry is often called the "language of the universe," and understanding it can help you appreciate everything from architecture to art!