The area of a rectangle is $14$ square units. It has side lengths $x$ and $y$ . Given each value for $x$ , find $y$ . $\newline$ a. $x=2\frac{1}{3}$ $\newline$ b. $x=4\frac{1}{5}$ $\newline$ c. $x=\frac{7}{6}$

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Q. The area of a rectangle is

14

square units. It has side lengths

x

and

y

. Given each value for

x

, find

y

\newline

x=2\frac{1}{3}

\newline

x=4\frac{1}{5}

\newline

x=\frac{7}{6}

Area Formula: The area of a rectangle is given by the formula $A = x \times y$ , where $A$ is the area, $x$ is one side length, and $y$ is the other side length. We are given that $A = 14$ square units.
Calculate $y$ for $a$ . For $a$ when $x = \frac{7}{3}$ , we can find $y$ by rearranging the area formula to $y = \frac{A}{x}$ . So $y = \frac{14}{\frac{7}{3}}$ .
Calculate $y$ for $b.$ : Calculating $y$ for $a.$ , we get $y = \frac{14}{\left(\frac{7}{3}\right)} = 14 \times \left(\frac{3}{7}\right) = 6$ . So when $x = \left(\frac{7}{3}\right)$ , $y = 6$ .
Calculate $y$ for $c$ : For $b$ when $x = \frac{21}{5}$ , we find $y$ by using the formula $y = \frac{A}{x}$ again. So $y = \frac{14}{\left(\frac{21}{5}\right)}$ .
Calculate $y$ for $c$ : For $b$ when $x = (21/5)$ , we find $y$ by using the formula $y = A / x$ again. So $y = 14 / (21/5)$ .Calculating $y$ for $b$ , we get $y = 14 / (21/5) = 14 \times (5/21) = 10/3$ . So when $x = (21/5)$ , $c$ $1$ .
Calculate y for c.: For b. when $x = \frac{21}{5}$ , we find y by using the formula $y = \frac{A}{x}$ again. So $y = \frac{14}{\frac{21}{5}}$ .Calculating y for b., we get $y = \frac{14}{\frac{21}{5}} = 14 \times \frac{5}{21} = \frac{10}{3}$ . So when $x = \frac{21}{5}$ , $y = \frac{10}{3}$ .For c. when $x = \frac{7}{6}$ , we find y by using the formula $y = \frac{A}{x}$ again. So $y = \frac{14}{\frac{7}{6}}$ .
Calculate $y$ for $c$ . For $b$ . when $x = \frac{21}{5}$ , we find $y$ by using the formula $y = \frac{A}{x}$ again. So $y = \frac{14}{\frac{21}{5}}$ .Calculating $y$ for $b$ ., we get $y = \frac{14}{\frac{21}{5}} = 14 \times \frac{5}{21} = \frac{10}{3}$ . So when $x = \frac{21}{5}$ , $c$ $1$ .For $c$ . when $c$ $3$ , we find $y$ by using the formula $y = \frac{A}{x}$ again. So $c$ $6$ .Calculating $y$ for $c$ ., we get $c$ $9$ . So when $c$ $3$ , $b$ $1$ .