Answer:
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.
