Taking l and w as the length and the width of the rectangle respectively, we have that:
[tex]w=l-3[/tex]
We know that the area of a rectangle is:
[tex]A=w\cdot l[/tex]
Replace A for the given value of the area and w for the expression stated:
[tex]54=(l-3)\cdot l[/tex]
Solve the operations and write the equation as a quadratic expression:
[tex]\begin{gathered} 54=l^2-3l \\ 0=l^2-3l-54 \end{gathered}[/tex]
Solve the quadratic equation using factorization:
[tex]\begin{gathered} 0=(l-9)(l+6) \\ l-9=0 \\ l=9 \\ l+6=0 \\ l=-6 \end{gathered}[/tex]
For this context, the value of l that we can use is 9. It means that the length of the triangle is 9m.
Use this value and the first expression to find w:
[tex]\begin{gathered} w=l-3 \\ w=9-3 \\ w=6 \end{gathered}[/tex]
The width of the triangle is 6m.
