Question

modeling real life an exercise mat is 3.3 times as long as it is wide. write expressions in simplest form that represent the perimeter and the area of the exercise mat. use the variable w to represent the width of the mat. an expression for the perimeter is . an expression for the area is .

Explanation:

Step1: Determine the length

Since the length of the exercise - mat is 3.3 times as long as it is wide and the width is \(w\), the length \(l = 3.3w\).

Step2: Find the perimeter formula

The perimeter \(P\) of a rectangle is \(P=2(l + w)\). Substitute \(l = 3.3w\) into the formula: \(P = 2(3.3w+w)\). Combine like - terms: \(P = 2(4.3w)=8.6w\).

Step3: Find the area formula

The area \(A\) of a rectangle is \(A=l\times w\). Substitute \(l = 3.3w\) into the formula: \(A=(3.3w)\times w = 3.3w^{2}\).

Answer:

Expression for the perimeter: \(8.6w\)
Expression for the area: \(3.3w^{2}\)