anonymous
  • anonymous
Paulina is remodeling her bathroom. The tile she has chosen is shown below. There are squares and trapezoids in the tile. The side length of each square in the tile is x centimeters. The height and the length of one of the bases of each trapezoid is x centimeters. The other length is 2x centimeters. a. Write a simplified equation to solve for x in terms of AT, the area of the tile. If necessary, use rational coefficients instead of root symbols. Type your response here:
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
chestercat
  • chestercat
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mathstudent55
  • mathstudent55
|dw:1450061440127:dw|
mathstudent55
  • mathstudent55
For the square: \(A_s = x^2\) For the trapezoid: \(A_t = \dfrac{(x + 2x)x}{2} =\dfrac{3x^2}{2}\)
anonymous
  • anonymous
Can I send you the activity so you can see it, the picture did not show up on here

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anonymous
  • anonymous
@mathstudent55
mathstudent55
  • mathstudent55
Is the figure similar to mine?
anonymous
  • anonymous
no
anonymous
  • anonymous
@mathstudent55
mathstudent55
  • mathstudent55
Are the dimensions in my figure the same as in your figure? I did follow what you wrote above.
mathstudent55
  • mathstudent55
A square with side x has area x^2. A trapezoid with bases x and 2x, has an average base length of (3x)/2. Then you multiply by the height x to get the area (3x^2)/2.
mathstudent55
  • mathstudent55
Now you need to solve each area formula for x.
mathstudent55
  • mathstudent55
BTW, you wrote this above: \(\sf "If~ necessary, ~use ~rational ~coefficients ~instead ~of ~root ~symbols."\) Did you mean: \(\sf "...~use ~rational ~\color{red}{exponents} ~instead ~of ~root ~symbols."\)?
anonymous
  • anonymous
anonymous
  • anonymous
@mathstudent55
mathstudent55
  • mathstudent55
Oh, I see. The tile is that entire thing made up of 4 squares and 8 trapezoids.
mathstudent55
  • mathstudent55
|dw:1450064234119:dw|
mathstudent55
  • mathstudent55
That means the total area of the tile is: \(A_T = 4x^2 + 8\left( \dfrac{3x^2}{2} \right) \) \(A_T = 4x^2 + 4 (3x^2) \) \(A_T = 4x^2 + 12x^2 \) \(A_T = 16x^2\)
mathstudent55
  • mathstudent55
Of course, if I had started with your drawing, I wold have done this: |dw:1450064500451:dw| Area of entire tile: \(A_T = (4x)^2 = 16x^2\)
mathstudent55
  • mathstudent55
\(A_T = 16x^2\) Now we solve for x: \(16x^2 = A_t\) \(x^2 = \dfrac{A_T}{16} \) \(x = \dfrac{\sqrt{A_T}}{4} = \dfrac{(A_T)^{\frac{1}{2}}}{4} \)
anonymous
  • anonymous
so if the side lenght is 6 then what would you do? @mathstudent55
anonymous
  • anonymous
do you plug in 6 for x?

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