Question

6 the goode family built a rectangular swimming pool in their backyard. the floor of the pool ha an area of $485\frac{5}{8}$ square feet. if the width of th pool is $18\frac{1}{2}$ feet, what is the length of the poo a $13\frac{1}{8}$ ft b $224\frac{5}{16}$ ft c $8,984\frac{1}{16}$ ft d $26\frac{1}{4}$ ft

Explanation:

Step1: Recall the formula for the area of a rectangle

The area \( A \) of a rectangle is given by \( A = l \times w \), where \( l \) is the length and \( w \) is the width. To find the length, we can rearrange the formula to \( l=\frac{A}{w} \).

Step2: Convert mixed numbers to improper fractions

First, convert the area \( 485\frac{5}{8} \) to an improper fraction.
\( 485\frac{5}{8}=\frac{485\times8 + 5}{8}=\frac{3880+5}{8}=\frac{3885}{8} \)
Next, convert the width \( 18\frac{1}{2} \) to an improper fraction.
\( 18\frac{1}{2}=\frac{18\times2+1}{2}=\frac{36 + 1}{2}=\frac{37}{2} \)

Step3: Divide the area by the width to find the length

Now, we need to find \( l=\frac{\frac{3885}{8}}{\frac{37}{2}} \). When dividing fractions, we multiply by the reciprocal of the divisor. So, \( l=\frac{3885}{8}\times\frac{2}{37} \)
Simplify the fractions: \( \frac{3885\times2}{8\times37}=\frac{3885}{4\times37} \)
Calculate \( 3885\div37 \): \( 37\times105 = 3885 \) (since \( 37\times100 = 3700 \), \( 37\times5=185 \), \( 3700 + 185=3885 \))
So now we have \( \frac{105}{4} \)

Step4: Convert the improper fraction back to a mixed number

\( \frac{105}{4}=26\frac{1}{4} \) (because \( 105\div4 = 26 \) with a remainder of \( 1 \))

Answer:

D. \( 26\frac{1}{4}\text{ ft} \)