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A 30 foot by 24 foot carpet has a white center whose area is 432 square feet. The carpet also has a dark grey border and the top, bottom, and side parts of this border have the same width,

a.

Write an equation using the variable that would allow you to find the width of the border.

b.

Solve your equation to find the width of the border. Show your work. Include proper units in your

answer. Write your final answer in the shaded box.
WILL GIVE BRAINLIEST PLEASE HELPN ANSWER

A 30 foot by 24 foot carpet has a white center whose area is 432 square feet The carpet also has a dark grey border and the top bottom and side parts of this bo class=

Respuesta :

Answer:

a) (30 - 2x) * (24 - 2x) = 432

b) 3 inches

Step-by-step explanation:

Let's call the width of the border 'x'.

So the length of the white center is 30 - 2x, and the width is 24 - 2x.

Then, we have that the white center area is:

(30 - 2x) * (24 - 2x) = 432

720 - 108x + 4x2 = 432

4x2 - 108x + 288 = 0

x2 - 27x + 72 = 0

Using Bhaskara's formula to solve the quadratic equation, we have:

Delta = 27^2 - 288 = 441

sqrt(Delta) = 21

x1 = (27 + 21)/2 = 24 (Not a reasonable answer, as the length and width of the center area would be negative)

x2 = (27 - 21)/2 = 3

So the dark grey border has a width of 3 inches

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