Answer:
length: 9 ft
width: 2 ft
Step-by-step explanation:
This can be worked using a quadratic equation, or it can be worked by considering factors of the area value.
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<h3>difference in dimensions</h3>
The difference in length between the long side (x+3) and the short side (x-4) is ...
(x +3) -(x -4) = 3+4 = 7 . . . . feet
<h3>area factors</h3>
The area formula is ...
A = LW
The given area is 18 square feet, so we want to find numbers that multiply to give 18 and that differ by 7 in their values. Here are the integer factors of 18:
18 = 1×18 = 2×9 = 3×6
Of these factor pairs, the values 2 and 9 differ by 7.
The garden is 9 feet long and 2 feet wide.
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<em>Additional comment</em>
We can check to see if these numbers are consistent with the given expressions:
x+3 = 9 ⇒ x = 6
x -4 = 6 -4 = 2 . . . . the other dimension we found
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If you solve this using a quadratic equation, you will find that dimensions -2 ft and -9 ft also pop out. That is x +3 = -2, or x = -5 is also a solution to the quadratic. Of course, that is an extraneous solution, which we avoid by considering only positive factors of 18.
The quadratic equation we're referring to is A=18 ⇒ (x+3)(x-4) = 18.
