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Musya8 [376]
2 years ago
13

Owen’s rectangular garden has a length of (x+3) feet and a width of (x−4) feet. If the area of the garden is 18 square feet, wha

t are the dimensions of the garden?
Mathematics
2 answers:
taurus [48]2 years ago
7 0

Answer:

length: 9 units width: 2 units

Step-by-step explanation:

The formula to find the area of a rectangle is length*width (LW)

x+3 is the length and x-4 is the width; together they multiply up to 18

(x+3)(x-4) = 18

x^2 - 4x + 3x - 12 = 18 (multiply it out using FOIL)

x^2 - x - 12 = 18 (combine like terms on the left side)

x^2 - x -30 = 0 (subtract 18 from both sides so that the right side is 0)

<em>Think what two numbers multiply up -30 and add up to -1 (5 and -6)</em>

(x+5)(x-6) = 0 (factor it)

x+5 = 0 and x-6 = 0 (solve using zero-product property)

x = -5 and x = 6 (solve)

x = 6 (only this one works since you cannot have a negative side length)

(6+3)(6-4) = 18 ? (plug in to find side lengths and check)

9 * 2 = 18 (Correct!)

Alexxandr [17]2 years ago
6 0

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.

__

<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.

_____

<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

__

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.

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Sauron [17]

Answer:

<h2>61°</h2>

Step-by-step explanation:

Use the sine law:

\dfrac{MO}{\sin(\angle N)}=\dfrac{NM}{\sin(\angle O)}

We have:

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Substitute:

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Studentka2010 [4]

Answer:

x=10

Step-by-step explanation:

Supplementary angles are angles equal to 180°.

Therefore:

4(2x+9)+2(4x-8)=180

Now that we have our equation, let's distribute the 4 and the 2 into the parentheses they are next to:

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Combine like terms:

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Subtract 20 from both sides of the equation:

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Divide by the coefficient of x, which is 16:

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Check your work by substituting 10 into one of the equations above:

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