Question

1. simplify an expression for the perimeter of the rectangle.

3w
5w - 2
perimeter:
8.
\frac{3}{4}r + 2r + \frac{1}{2}r
9.
1.5r - 3r + 8r + 2.5r
10.
\frac{2}{3}p + \frac{4}{3}p - \frac{1}{3}p

Explanation:

Step1: Recall the formula for the perimeter of a rectangle

The perimeter \(P\) of a rectangle is given by \(P = 2(l + w)\), where \(l\) is the length and \(w\) is the width. Here, \(l=5w - 2\) and \(w = 3w\).

Step2: Substitute the values of length and width into the formula

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Step3: Simplify the expression inside the parentheses

Combine like - terms: \(5w+3w=8w\). So, \(P = 2(8w - 2)\)

Step4: Distribute the 2

Using the distributive property \(a(b + c)=ab+ac\) (here \(a = 2\), \(b = 8w\), \(c=-2\)), we get \(P=2\times8w-2\times2\)

$$P = 16w-4$$

Answer:

\(16w - 4\)