Acompany manufactures rectangular wooden frames. one particular frame has inside dimensions of 10cm by 15cm. find the width, x cm, of wood in the frame which will make the area of the frame itself equal to 116cm²

  2 cm

Step-by-step explanation:

The outside dimensions of the frame are 2x more than the inside dimensions, so the overall area is ...

  (10 +2x)(15 +2x) = 150 +50x +4x^2

Subtracting the inside area, we find the wood area to be ...

  wood area = outside area - inside area

  wood area = 4x^2 +50x +150 - 150

  116 = 4x^2 +50x . . . . simplify and fill in value for wood area

Dividing by 4, we get

  29 = x^2 +12.5x

Completing the square gives ...

  29 +39.0625 = x^2 +12.5x +39.0625

  68.0625 = (x +6.25)^2

  8.25 = x +6.25 . . . . . . taking the positive square root

  2.00 = x . . . . . . . . . . . .subtract 6.25

The width of the wood is 2 cm to make the area of the frame equal to 116 cm^2.