Hi Student!
Looking at the picture that was provided, we see that the problem statement is asking for us to determine the perimeter of the shape is. Perimeter is the outer layer of the shape which would include the lengths of all the sides that are exposed to the outside.
In this case, we are given 7 different values which represent each of the different sides of the shape which we need to add together to get the perimeter.
Create an expression
- [tex]\textsf{Perimeter = side_{1}}[/tex][tex]\textsf{Perimeter = side1 + side2 + side3 + side4 + side5 + side6 + side7}[/tex]
Using the expression above, all we need to do is combine all of the values which will give us the outline on our shape. However, since some of the values have different denominators, we will first need to combine the whole numbers and then combine those with a common denominator and finally apply a common denominator to be able to add the rest.
Combine the whole numbers
- [tex]\textsf{Perimeter = }35\frac{3}{7} + 10\frac{1}{7} + 10\frac{1}{7} + 12\frac{2}{7} + 12\frac{2}{7} + 15\frac{3}{14} + 24\frac{1}{14}[/tex]
- [tex]\textsf{Perimeter = }(35 + 10 + 10+12+12+15+24)+(\frac{3}{7} + \frac{1}{7} + \frac{1}{7} + \frac{2}{7} + \frac{2}{7} + \frac{3}{14} + \frac{1}{14})[/tex]
- [tex]\textsf{Perimeter = }(118)+(\frac{3}{7} + \frac{1}{7} + \frac{1}{7} + \frac{2}{7} + \frac{2}{7} + \frac{3}{14} + \frac{1}{14})[/tex]
Combine those with a common denominator
- [tex]\textsf{Perimeter = }(118)+(\frac{3}{7} + \frac{1}{7} + \frac{1}{7} + \frac{2}{7} + \frac{2}{7}) + (\frac{3}{14} + \frac{1}{14})[/tex]
- [tex]\textsf{Perimeter = }(118)+(\frac{3+1+1+2+2}{7}) + (\frac{3+1}{14})[/tex]
- [tex]\textsf{Perimeter = }(118)+(\frac{9}{7}) + (\frac{4}{14})[/tex]
Covert to mixed fraction and simplify
- [tex]\textsf{Perimeter = }(118)+(1\frac{2}{7}) + (\frac{4}{14})[/tex]
- [tex]\textsf{Perimeter = }(119)+(\frac{2}{7}) + (\frac{4}{14})[/tex]
Find common denominator and combine
- [tex]\textsf{Perimeter = }(119)+(\frac{2*2}{7*2}) + (\frac{4}{14})[/tex]
- [tex]\textsf{Perimeter = }(119)+(\frac{4}{14}) + (\frac{4}{14})[/tex]
- [tex]\textsf{Perimeter = }(119)+(\frac{4}{14}+\frac{4}{14})[/tex]
- [tex]\textsf{Perimeter = }(119)+(\frac{4+4}{14})[/tex]
- [tex]\textsf{Perimeter = }(119)+(\frac{8}{14})[/tex]
Simplify the expression
- [tex]\textsf{Perimeter = }(119)+(\frac{8/2}{14/2})[/tex]
- [tex]\textsf{Perimeter = }(119)+(\frac{4}{7})[/tex]
- [tex]\textsf{Perimeter = }119\frac{4}{7}[/tex]
Therefore, the final answer for the perimeter of the figure that was provided would be [tex]119\frac{4}{7}[/tex] units.
