Given:
Area of the rectangle is 50 sq. m.
The length of the rectangle is 5 m less than three times the width.
That is,
l=3w-5
To find the dimensions:
The formula for the area of the rectangle is , A=lw
Therefore,
[tex]\begin{gathered} A=(3w-5)() \\ 50=3w^2-5w \\ 3w^2-5w-50=0 \\ (3w-15)(3w+10)=0 \\ 3w=15,3w=-10 \\ w=5,w=-\frac{10}{3} \end{gathered}[/tex]Since, width can not be negative.
So, -10/3 can be neglected.
Hence, w=5
So, the length is,
[tex]\begin{gathered} l=3(5)-5_{} \\ =15-5 \\ =10 \end{gathered}[/tex]Hence, the dimensions are, l=10 m and w=5 m.
