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Mrs. Jacinto asked a carpenter to construct a rectangular bulletin board for her classroom. She told the carpenter that the board’s area must be 18 square feet.
Q.)
1.)Draw a diagram to illustrate the bulletin board. 
2.)What are the possible dimensions of the bulletin board? Give at least 2 pairs of possible dimensions. 
3.)How did you determine the possible dimensions of the bulletin board? \
4.)Suppose the length of the board is 7 ft. longer than its width. What equation would represent the given situation? 
5.)How would you describe the equation formulated?
6.)Do you think you can use the equation formulated to find the length and the width of the bulletin board? Justify your answer. 

Please Help me Guyx ... TT^TT

Sagot :

glendzmorales

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

#BetterWithBrainly

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