42 ³/₄ ft²
Given:
Question:
What is the area?
The Process:
A gardening box is rectangular. Units of length that are the same, i.e., in feet.
The perimeter formula is as follows:
[tex]\boxed{ \ Perimeter = length + length + width + width \ }[/tex]
It can also be written as follows:
[tex]\boxed{\boxed{ \ Perimeter = 2 \times (length + width) \ }}[/tex]
Step-1: calculate the width
Let's use the formula above.
[tex]\boxed{ \ 2 \times (9 + width) = 27\frac{1}{2} \ }[/tex]
[tex]\boxed{ \ 9 + width = \frac{55}{2} \div 2 \ }[/tex]
[tex]\boxed{ \ 9 + width = \frac{55}{2} \times \frac{1}{2} \ }[/tex]
[tex]\boxed{ \ 9 + width = \frac{55}{4} \ }[/tex]
[tex]\boxed{ \ width = \frac{55}{4} - 9 \ }[/tex]
[tex]\boxed{ \ width = \frac{55}{4} - \frac{36}{4} \ }[/tex]
[tex]\boxed{\boxed{ \ width = \frac{19}{4} \ ft\ }}[/tex]
Step-2: calculate the area
The area formula is as follows:
[tex]\boxed{\boxed{ \ Area = length \times width \ }}[/tex]
[tex]\boxed{ \ Area = 9 \times \frac{19}{4} \ }[/tex]
[tex]\boxed{ \ Area = \frac{171}{4} = 42\frac{3}{4} \ }[/tex]
Thus, the area of a gardening box is [tex]\boxed{\boxed{ \ 42\frac{3}{4} \ ft^2 \ }}[/tex]
Keywords: a gardening box, has a perimeter, 27 1/2 feet, the length, width, 9 feet, what is the area?, rectangular, formula
