Question

Find the perimeter.

15 24/14
14
10/
12²/
12/3/1
10/1/
35 -/-/
Perimeter = 119
Simplify your answer completely.
?

Answer 1

let's firstly convert the mixed fractions to improper fractions and then add them up.

`\stackrel{mixed}{10(1)/(7)}\implies \cfrac{10\cdot 7+1}{7}\implies \stackrel{improper}{\cfrac{71}{7}} ~\hfill \stackrel{mixed}{12(2)/(7)}\implies \cfrac{12\cdot 7+2}{7}\implies \stackrel{improper}{\cfrac{86}{7}} \\\\\\ \stackrel{mixed}{15(3)/(14)}\implies \cfrac{15\cdot 14+3}{14}\implies \stackrel{improper}{\cfrac{213}{14}} ~\hfill \stackrel{mixed}{24(1)/(14)}\implies \cfrac{24\cdot 14+1}{14}\implies \stackrel{improper}{\cfrac{337}{14}}`

`\stackrel{mixed}{35(3)/(7)}\implies \cfrac{35\cdot 7+3}{7}\implies \stackrel{improper}{\cfrac{248}{7}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{71}{7}+\cfrac{71}{7}+\cfrac{86}{7}+\cfrac{86}{7}+\cfrac{213}{14}+\cfrac{337}{14}+\cfrac{248}{7}\hspace{5em}\textit{so we have an LCD of 14} \\\\\\ \cfrac{(2)71+(2)71+2(86)+2(86)+(1)213+(1)337+2(248)}{14} \\\\\\ \cfrac{1674}{14}\implies \cfrac{837}{7}\implies 119(4)/(7)`

Answer 2

`\displaystyle\\Answer:\ 119\ \boxed{(4)/(7) }`

Explanation:

`\displaystyle\\P=10(1)/(7)+12(2)/(7)+15(3)/(14) +24(1)/(14) +12(2)/(7) +10(1)/(7)+35(3)/(7) \\\\P=(10(1)/(7)+12(2)/(7)+12(2)/(7) +10(1)/(7)+35(3)/(7))+(15(3)/(14) +24(1)/(14)) \\\\P=((71)/(7) +(86)/(7) +(86)/(7)+(71)/(7) +(248)/(7) )+((213)/(14)+(337)/(14))\\\\`

`\displaystyle\\ P=(71+86+86+71+248)/(7) +(213+337)/(14) \\\\P=(562)/(7) +(550)/(14) \\\\P=(562)/(7)+(2(275))/(2(7)) \\\\P=(562)/(7) +(275)/(7)\\\\P=(562+275)/(7) \\\\P=(837)/(7)\\\\P=119(4)/(7)`