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If the side length of a square can be represented by 4x+ 3 and its area is 121 square units, find the value of x.

User SleepToken
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Final answer:

To find the value of x when the side length of a square is 4x + 3 and the area is 121 square units, you set up and solve the equation (4x + 3)² = 121. The solution is x = 2.

Step-by-step explanation:

If the side length of a square is represented by 4x + 3 and its area is 121 square units, to find the value of x, we can set up the equation:

(4x + 3)2 = 121

By solving the equation:

  1. Expand the left side: (4x + 3)(4x + 3) = 16x2 + 12x + 12x + 9
  2. Simplify: 16x2 + 24x + 9 = 121
  3. Subtract 121 from both sides: 16x2 + 24x - 112 = 0
  4. Divide all terms by 8: 2x2 + 3x - 14 = 0
  5. Factor the quadratic: (2x + 7)(x - 2) = 0
  6. Solve for x: x = -7/2 or x = 2
  7. Since a side length cannot be negative, the value of x must be 2.

User Dilip Krishnan
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