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Your school wants to take out an ad in the paper congratulating the basketball team on a successful season, as shown to the right. The area of the photo will be half the area of the entire ad. What is the value of X?

Your school wants to take out an ad in the paper congratulating the basketball team-example-1

1 Answer

5 votes

Answer:

  • - 6 + 2√17 or approximately 2.25 in

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The area of the photo is:

  • A(photo) = 8*4 = 32 in²

Area of the ad is:

  • A(ad) = (8 + x)(4 + x) = x² + 12x + 32

Area of the photo is half the area of the entire ad:

  • 32 = (x² + 12x + 32)/2
  • 64 = x² + 12x + 32
  • x² + 12x - 32 = 0
  • x = (-12 ± √(12² - 4(-32)))/2
  • x = -6 ± 2√17

Only positive root makes sense:

  • x = - 6 + 2√17 ≈ 2.25
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