To solve this question, we first need to understand what it means when we say that the width is 200% of the length. When we say 200%, it means two times (or double) the referenced amount. Here, the length is our reference.
Let's denote the length of the field as [tex]\( L \)[/tex]. Now, according to the information provided, the width (which we'll denote as [tex]\( W \)[/tex]) is 200% of the length, which means:
[tex]\[ W = 200\% \times L \][/tex]
Since 200% is equal to 2 (when you convert percentage to a decimal, you divide by 100, so 200% becomes [tex]\(2.00\)[/tex] or simply [tex]\(2\)[/tex]), we can simplify this to:
[tex]\[ W = 2 \times L \][/tex]
Moving on to find the difference between the width and the length, we subtract the length from the width:
[tex]\[ \text{Difference} = W - L \][/tex]
Plugging in our expression for [tex]\( W \)[/tex] from above, we get:
[tex]\[ \text{Difference} = (2 \times L) - L \][/tex]
When we carry out the multiplication and subtraction, we’re left with:
[tex]\[ \text{Difference} = 2L - L \][/tex]
[tex]\[ \text{Difference} = L \][/tex]
Meaning, the difference between the length and the width is exactly equal to the length of the field.
Assuming the length of the field is 1 unit (since no specific measurement was provided), the width would therefore be:
[tex]\[ W = 2 \times 1 \][/tex]
[tex]\[ W = 2 \][/tex]
And the difference would be:
[tex]\[ \text{Difference} = 2 - 1 \][/tex]
[tex]\[ \text{Difference} = 1 \][/tex]
So, the width of the field is 2 units and the length is 1 unit, making the difference between the width and the length of the field 1 unit.
