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  • Brainly User
2016-03-07T08:39:09+08:00

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Dimension:
     Width: x
     Length: 2x + 3
     Area: 560 sq. inches

Area = Length x Width

Equation:
   (2x + 3) (x) = 560

   2x² + 3x = 560

Transform to quadratic equation, ax² + bx + c = 0:
     2x² + 3x - 560 = 0

Use Quadratic formula to solve for x:
     a = 2     b = 3      c = -560

   x₁,₂ =  \frac{-(3)  \frac{+}{-}  \sqrt{(3) ^{2}-4(2)(-560) } }{2(2)}

   x₁,₂ =  \frac{-3  \frac{+}{-}  \sqrt{9+4,480 } }{4}

   x₁,₂ =  \frac{-3  \frac{+}{-} \sqrt{4489}  }{4}

   x₁ =  \frac{-3 +67}{4}

   x₁ = 64/4

   x₁ = 16

------------------- 

   x₂ =  \frac{-3 -67}{4}

   x₂ = -70/4    or   -35/2

Choose the positive root, x₁ = 16

Substitute 16 for x in dimension:
   Width:x = 16 inches
   Length: 2x + 3 = 2(16) + 3 = 35 inches

ANSWER:  Length is 35 inches and width is 16 inches.

Check:
   (35 inches) (16 inches) = 560 sq. inches
   560 sq. inches = 560 sq. inches  (true)

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