Answer:
1. The diagrams of the bulletin board were shown below.
2. The possible dimensions of the bulletin board are 3 ft x 6 ft and 2 ft x 9 ft.
3. The possible dimensions were determined by getting the factors of 18.
4. [tex]W^2 + 7W -18=0[/tex]
5. It is a quadratic equation.
6. Yes. Using quadratic equation to solve for W then substitute the value of W to L=W+7 to solve for the length.
Step-by-step explanation:
Formula of rectangle
A = L x W
For the given information:
A = 18 sq. ft.
L = ?
W = ?
2 - 3. The possible dimensions of the bulletin were simply taken from the factors of 18.
A = L x W
Substitute 18 to the formula, we get:
18 = L x W Now, think for the possible factors of 18
a. 18 = 3 x 6
b. 18 = 2 x 9
4. Represent the length of the board 7 ft longer than its width
L = W + 7 equation 1
Substitute equation 1 to the area of a rectangle
A = L x W
A = (W + 7)(W)
[tex]18=W^{2} +7W[/tex]
Using the standard form of a quadratic equation,
[tex]W^2 + 7W -18=0[/tex]
5. The description of [tex]W^2 + 7W -18=0[/tex] is a quadratic equation where W can be solved.
Solving the problem
[tex]W^2 + 7W -18=0[/tex]
Using quadratic equation
[tex]W=\frac{-7+\sqrt{7^2-4(1)(-18)} }{2(1)}[/tex]
[tex]W=\frac{-7+\sqrt{49+72} }{2}[/tex]
[tex]W=\frac{-7+11}{2}[/tex]
[tex]W=\frac{4}{2} =2[/tex]
Substitute [tex]W=2[/tex] to equation 1
L = W + 7
L = 2 + 7
L = 9
Therefore, the dimensions of the rectangular bulletin board is 9 ft x 2 ft.
6. Through the use of quadratic formula, we were able to solve for the dimensions of the rectangular bulletin board.
To learn more about area of a rectangle, just click on the following links below:
* How to find the area of a rectangle
https://brainly.ph/question/110308
* Additional example
https://brainly.ph/question/2004152
https://brainly.ph/question/537312
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