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A rectangular vegetable garden will have a width that is 2 feet less than the length, and an area of 48 square feet. If x represents the length, then the length can be found by solving the equation:

What is the length, x, of the garden?

User Jgreve
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1 Answer

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Explanation:

x = length

y = width

x×y = 48 ft²

y = x - 2

using the second in the first equation we get

x × (x - 2) = 48

x² - 2x - 48 = 0

we can solve this quickly by finding the factors of -48 that are only 2 apart in their absolute value, and the negative factor must be 2 larger in its absolute value than the positive one.

simply because

(a + b)(a - c) = a² - ac + ab - bc

-bc = -48

-ac + ab = -2x

a = x

-c + b = -2

and so we see, 48 = 6×8 (2 difference between the factors).

the larger number must be negative, so, -8×6

and we get

(x + 6)(x - 8)

therefore, the solutions are

x = -6 and x = 8

a negative length does not makes sense here, so x = 8 is or solution.

the length of the garden is 8 ft.

the width is 8 - 2 = 6 ft.

User The Roy
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