Answer: x = 8
The diagram is shown below.
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Step-by-step explanation:
Use the SAS triangle area formula to get the following equation.
area = 0.5*side1*side2*sin( angle between those sides)
area = 0.5*AB*AC*sin( angle BAC )
area = 0.5*(x+1)*x*sin(30)
area = 0.5x(x+1)*0.5
area = 0.25x^2+0.25x
Set this equal to the stated area of 18 square cm and solve for x.
0.25x^2+0.25x = 18
4*(0.25x^2+0.25x) = 4*18
x^2+x = 72
x^2+x-72 = 0
(x-8)(x+9) = 0
x-8 = 0 or x+9 = 0
x = 8 or x = -9
Ignore the negative value since we cannot have a negative side length.
The only possible outcome is that x = 8 which leads to x+1 = 8+1 = 9.
The diagram is below.