Question

1. use structure mr. wells drew a plan for a rectangular dog run. the vertices are $(2\frac{1}{3},7\frac{1}{2}),(12,7\frac{1}{2}),(12,1)$, and $(2\frac{1}{3},1)$. what is the perimeter of the dog run?

Explanation:

Step1: Find the length of the rectangle

The length \( l \) can be found by subtracting the \( x - \)coordinates of two points with the same \( y - \)coordinate. Using the points \((2\frac{1}{3},7\frac{1}{2})\) and \((12,7\frac{1}{2})\).

$$l = 12 - 2\frac{1}{3}=12-\frac{7}{3}=\frac{36 - 7}{3}=\frac{29}{3}$$

Step2: Find the width of the rectangle

The width \( w \) can be found by subtracting the \( y - \)coordinates of two points with the same \( x - \)coordinate. Using the points \((12,7\frac{1}{2})\) and \((12,1)\).

$$w=7\frac{1}{2}-1=\frac{15}{2}-1=\frac{15 - 2}{2}=\frac{13}{2}$$

Step3: Use the perimeter formula for a rectangle

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

$$P = 2(\frac{29}{3}+\frac{13}{2})$$

First, find a common denominator (which is \(6\)):

$$\frac{29}{3}+\frac{13}{2}=\frac{29\times2}{3\times2}+\frac{13\times3}{2\times3}=\frac{58}{6}+\frac{39}{6}=\frac{58 + 39}{6}=\frac{97}{6}$$

Then, \(P = 2\times\frac{97}{6}=\frac{97}{3}=32\frac{1}{3}\)

Answer:

\(32\frac{1}{3}\)