A community center is expanding the size of its rectangular meeting hall. The hall is currently 300ft long and 150ft wide. The center plans to expand both the length and the width of the meeting hall by 3x ft. What polynomial in standard form represents the area of the expanded meeting hall?
Please explain how to set up and to solve. Thanks
before 300 x 150
now: (3x+300)(3x+150)
We expand this by multiplying the first two terms (3x and 3x)
Then add that to the first term of the first parentheses (now henceforth p) and the last term of the second p.
Then add that to the last term of the first p and the first term of the second p.
Then add that to the last terms of both p.
= 9x^2 + 450x+900x + 45000 =
9x^2 + 1350 x + 45000
That's your answer.
Thank You for the answer.
Well, well, well, if it isn't the expanding community center with its rectangular meeting hall. It seems like they want to give it a little growth spurt, huh? Alrighty, let's get to the bottom of this expansion.
So, the current length of the meeting hall is 300ft, and they want to expand it by an additional 3x feet. Therefore, the new length is 300ft + 3x.
Similarly, the current width is 150ft, and they want to expand it by an additional 3x feet. Therefore, the new width is 150ft + 3x.
To find the area of the expanded meeting hall, we multiply the length by the width. So the area can be found by:
Area = (300ft + 3x)(150ft + 3x)
We can use the distributive property to expand the expression:
Area = 300ft * 150ft + 300ft * 3x + 150ft * 3x + 3x * 3x
Area = 45,000ft² + 900ftx + 450ftx + 9x²
Combining like terms, we get the polynomial in standard form:
Area = 9x² + 1350ftx + 45,000ft²
And there you have it! The polynomial in standard form that represents the area of the expanded meeting hall. Now that's some serious math circus!
To find the polynomial that represents the area of the expanded meeting hall, let's first define the increase in length and width as "3x" (in feet).
The original length of the meeting hall is 300ft, and we want to increase it by 3x ft. Therefore, the new length will be 300ft + 3x ft.
Similarly, the original width is 150ft, and we want to increase it by 3x ft. Hence, the new width will be 150ft + 3x ft.
The area of a rectangle is calculated by multiplying its length by its width. Thus, the area of the expanded meeting hall can be represented by the polynomial:
Area = (300ft + 3x ft) * (150ft + 3x ft)
To remove the parentheses and simplify the equation, we will use the distributive property:
Area = 300ft * 150ft + 300ft * 3x ft + 150ft * 3x ft + 3x ft * 3x ft
Simplifying each term:
Area = 45,000ft² + 900ft*x + 450ft*x + 9x²
Combining like terms, the polynomial representing the area of the expanded meeting hall in standard form is:
Area = 9x² + 1,350x + 45,000ft²
To find the polynomial that represents the area of the expanded meeting hall, we need to first determine the new length and width of the hall.
The length of the expanded hall can be found by adding 3x feet to the current length of 300 feet. So, the new length would be 300 + 3x feet.
Similarly, the width of the expanded hall can be found by adding 3x feet to the current width of 150 feet. So, the new width would be 150 + 3x feet.
The area of a rectangle can be calculated by multiplying its length by its width. Therefore, to find the polynomial representing the area of the expanded meeting hall, we need to multiply the new length by the new width.
Area = (300 + 3x)(150 + 3x)
Next, we can expand this expression using the distributive property:
Area = 300 * 150 + 300 * 3x + 150 * 3x + (3x * 3x)
Simplifying further:
Area = 45000 + 900x + 450x + 9x^2
Finally, we can arrange the terms in descending powers of x to express the polynomial in standard form:
Area = 9x^2 + 1350x + 45000
Therefore, the polynomial in standard form that represents the area of the expanded meeting hall is 9x^2 + 1350x + 45000.