Fencing material

Ailey bought 10 meters of wire fencing material to enclose her triangular flower garden. If the lengths of the sides of the triangular garden are 2 ½ meters, 3 ⅔ meters, 2 ⅙ meters, how long will the excess wire fencing material be?

Correct answer:

e =  1 ²⁄₃ = 5/3 m

Step-by-step explanation:

$$\begin{gathered} x=10\text{m} \\ a=2\frac{1}{2}=2+\frac{1}{2}=\frac{2\cdot 2+1}{2}=\frac{4+1}{2}=\frac{5}{2}=2.5\text{m} \\ b=3\frac{2}{3}=3+\frac{2}{3}=\frac{3\cdot 3+2}{3}=\frac{9+2}{3}=\frac{11}{3}\doteq 3.6667\text{m} \\ c=2\frac{1}{6}=2+\frac{1}{6}=\frac{2\cdot 6+1}{6}=\frac{12+1}{6}=\frac{13}{6}\doteq 2.1667\text{m} \\ o=a+b+c=\frac{5}{2}+\frac{11}{3}+\frac{13}{6}=\frac{15}{6}+\frac{22}{6}+\frac{13}{6}=\frac{15+22+13}{6}=\frac{50}{6}=\frac{25}{3}\doteq 8.3333\text{m} \\ e=x-o=10-\frac{25}{3}=\frac{10\cdot 3}{3}-\frac{25}{3}=\frac{30}{3}-\frac{25}{3}=\frac{30-25}{3}=\frac{5}{3}=\frac{5}{3}\text{m}=1\frac{2}{3}\text{m}=1.6667\text{m} \end{gathered}$$

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