SOLUTION
Step 1: List out the given parameters.
[tex]\begin{gathered} \text{Let the height be x} \\ \text{Base}=3x+1 \\ A=40m^2 \end{gathered}[/tex]Step 2: Write the formula for the area of the triangle and solve.
[tex]\begin{gathered} A=\frac{1}{2}\times\text{base x height} \\ \end{gathered}[/tex]Substitute the parameters in step 1 into the formula in step 2
[tex]\begin{gathered} 40=\frac{1}{2}\times(3x+1)\times x \\ 80=3x^2+x \\ 3x^2+x-80=0 \end{gathered}[/tex]Solving the above quadratic equation by quadratic formula method, we will get:
[tex]x=5\text{ and x=}\frac{-16}{3}[/tex]Since the value for a side of a triangle cannot be negative, x=5 is the only value of x we can use.
Therefore:
[tex]\begin{gathered} \text{height}=x=5m \\ \text{Base}=(3x+1)=(3(5)+1)=(15+1)=16m \end{gathered}[/tex]So we can conclude that:
The base is 16 meters and the height is 5 meters.
