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.
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
1 answer