Question

apply

1. a rectangle has a length that is half its width. define a variable to represent the unknown quantity. then write an expression to represent the perimeter of the rectangle.
2. in a triangle there are two sides that have the same length and the third side is 1.5 times longer than the length of the other two. define a variable to represent the unknown quantity. then write an algebraic expression to represent the perimeter of the triangle.
3. use structure write an expression that has four terms and at least one constant. identify the like terms, coefficients, and constants in your expression.
4. analyze problems if x represents the number of questions on a test, analyze the meaning of each expression: x + 4, x - 5, 2x, and x ÷ 3.
5. build perseverance norman earns $8 for every dog he washes plus 25% of the cost of the dog wash. write an expression that represents the total amount of money norman earns for one dog wash with a cost, c.
6. create write about a real - world situation that can be represented with an algebraic expression. then represent the situation with the expression.

Explanation:

Step1: Define the variable

Let \( w \) represent the width of the rectangle. Then the length \( l=\frac{1}{2}w \).

Step2: Recall the perimeter formula

The perimeter formula of a rectangle is \( P = 2(l + w) \).

Step3: Substitute the length into the formula

Substitute \( l=\frac{1}{2}w \) into \( P = 2(l + w) \), we get \( P=2(\frac{1}{2}w+w) \).

Step4: Simplify the expression

First, simplify the expression inside the parentheses: \( \frac{1}{2}w+w=\frac{1 + 2}{2}w=\frac{3}{2}w \). Then \( P = 2\times\frac{3}{2}w=3w \).

Answer:

Let \( w \) be the width of the rectangle. The expression for the perimeter is \( 3w \).