Question

juan is building an irregularly shaped garden that has a perimeter of $15\frac{1}{2}ft$. use the picture of his garden below to determine the length of the missing side. include units in your answer. $2\frac{2}{3}ft$ $3\frac{3}{4}ft$ $4\frac{1}{8}ft$

Explanation:

Step1: Convert mixed numbers to improper fractions

$15\frac{1}{2}=\frac{15\times2 + 1}{2}=\frac{31}{2}$, $2\frac{2}{3}=\frac{2\times3+2}{3}=\frac{8}{3}$, $3\frac{3}{4}=\frac{3\times4 + 3}{4}=\frac{15}{4}$, $4\frac{1}{8}=\frac{4\times8+1}{8}=\frac{33}{8}$

Step2: Let the missing side be $x$ and use the perimeter formula

Perimeter $P=a + b+ c + d$. So $\frac{31}{2}=\frac{8}{3}+\frac{15}{4}+\frac{33}{8}+x$

Step3: Find a common denominator (24) and simplify

$\frac{31\times12}{2\times12}=\frac{8\times8}{3\times8}+\frac{15\times6}{4\times6}+\frac{33\times3}{8\times3}+x$
$\frac{372}{24}=\frac{64}{24}+\frac{90}{24}+\frac{99}{24}+x$
$\frac{372}{24}=\frac{64 + 90+99}{24}+x$
$\frac{372}{24}=\frac{253}{24}+x$

Step4: Solve for $x$

$x=\frac{372}{24}-\frac{253}{24}=\frac{372 - 253}{24}=\frac{119}{24}=4\frac{23}{24}$

Answer:

$4\frac{23}{24}\text{ ft}$