Solve each problem. See Example 1. Michael must build a rectangular storage shed. He wants the length to be 6 ft greater than the width, and the perimeter will be 44 ft. Find the length and the width of the shed.

Verified step by step guidance

1. Let the width of the shed be $w$ feet.
2. Since the length is 6 feet greater than the width, express the length as $w+6$ feet.
3. The formula for the perimeter of a rectangle is $P=2(l+w)$.
4. Substitute the given perimeter (44 ft) and the expressions for length and width into the formula: $44=2((w+6)+w)$.
5. Simplify and solve the equation for $w$ to find the width, then use $w+6$ to find the length.

Key Concepts

Perimeter of a Rectangle

The perimeter of a rectangle is the total distance around the shape, calculated by the formula P = 2L + 2W, where L is the length and W is the width. Understanding this formula is essential for solving problems involving the dimensions of rectangular shapes, as it relates directly to the constraints given in the problem.

Algebraic Expressions

Algebraic expressions are mathematical phrases that can include numbers, variables, and operations. In this problem, the relationship between the length and width can be expressed as L = W + 6, which allows us to set up equations based on the given perimeter. Mastery of forming and manipulating these expressions is crucial for finding the unknown dimensions.

Solving Linear Equations

Solving linear equations involves finding the value of variables that satisfy the equation. In this context, once the perimeter equation is set up with the expressions for length and width, students will need to solve for W and subsequently for L. This skill is fundamental in algebra, as it enables the resolution of various mathematical problems.