Question

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?

Answer 1

• - 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