The area of the rectangle shown below is 5 1/4 m2 What is the width of the rectangle in meters? A 7m B 3 1/2m C 3m D 4 3/4m
Let the length of the rectangle be $l$ and the width be $w$. We are given that $lw=5 \frac{1}{4} = \frac{21}{4}$ square meters. We are asked to find $w$.
We can write the equation $lw = \frac{21}{4}$, and we can find $w$ by dividing both sides of the equation by $l$: $$\begin{aligned} \frac{l \cdot w}{l} &= \frac{\frac{21}{4}}{l} \\ w &= \frac{21}{4l} \end{aligned}$$Since the width of the rectangle is in meters, $w$ must be in meters. None of the answer choices are fractions or mixed numbers, so $w$ must also be an integer. We can test each of the answer choices (keeping in mind that $l$ must be an integer) to see which one satisfies the equation.
$\circ$ If $w=7$ meters, then $w = \frac{21}{4l} = \frac{1}{l}$. The fraction $\frac{1}{l}$ is always less than 1, so $\frac{21}{4l}$ cannot be equal to 7, which means that $w = 7$ meters does not work.
$\circ$ If $w=3 \frac{1}{2}$ meters, then $w = \frac{21}{4l} = \frac{7}{2l}$. The fraction $\frac{7}{2l}$ is always less than 1, so $\frac{21}{4l}$ cannot be equal to $\frac{7}{2}$. In addition, $\frac{21}{4l}$ will never be equal to any number with a fraction part, so $w = 3 \frac{1}{2}$ meters does not work.
$\circ$ If $w=3$ meters, then $w = \frac{21}{4l} = \frac{7}{l}$. However, we are looking for an integer value of $l$, and $\frac{7}{l}$ will not equal an integer when $l=1,2,3,4,5,6$. Thus, $w = 3$ meters does not work.
$\circ$ If $w=4 \frac{3}{4}$ meters, then $w = \frac{21}{4l}$. If we choose $l=3$, then $w = \frac{21}{4l} = \frac{21}{4(3)} = \frac{7}{4}$. Since $w$ is a fraction of a whole number, this is not a possible value for the width. If we choose $l=4$, then $w = \frac{21}{4l} = \frac{21}{4(4)} = \frac{21}{16}$. Since $w$ is a fraction of a whole number, this is not a possible value for the width. However, if we choose $l=2$, then $w = \frac{21}{4l} = \frac{21}{4(2)} = \frac{21}{8} = \frac{4}{8} = \frac{1}{2}$. Since $w$ is a fraction of a whole number, this is not a possible value for the width. Thus, $w = 4 \frac{3}{4}$ meters does not work.
None of the answer choices work, so there must be an error in the problem statement or the answer choices.