Answered

a gardening box has a perimeter of 27 1/2 feet. if the length is 9 feet, what is the area?



Answer :

To figure out the width is easy all you do is subtract the length twice, because of there being 2 sides that have the same length,and then divide whatever is left. So its 27.5-18=9.5. 9.5/2=4.75. 4.5 is your width. and now area. area=length times width, so a= 9 times 4,75, which is 42.75.

42 ³/₄ ft²

Further explanation

Given:

  • A gardening box has a perimeter of 27 ¹/₂ feet.
  • The length is 9 feet.

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]

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Keywords: a gardening box, has a perimeter, 27 1/2 feet, the length, width, 9 feet, what is the area?, rectangular, formula

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