We know from the problem that l = 3w - 5. We also know the formula for area is A = w * l. Therefore, the area of the rectangle is A = w * (3w - 5). We can then set this equation equal to 50 as the question states and solve for w.
[tex]50 = w*(3w - 5)[/tex]
Expand the multiplication
[tex]50 = 3w^2 - 5w[/tex]
Subtract 50 from both sides.
[tex]0 = 3w^2 - 5w - 50[/tex]
We now have a quadratic equation and can solve it using the quadratic formula to find w. We find that the solutions to the equation are 5 and -3.3. We know that the width can't be negative, so the width must be 5.
Finally, we can plug this solution into the length formula we found earlier to solve for length.
[tex]l = 3w - 5[/tex]
Plug in the solution to w.
[tex]l = 3(5) - 5[/tex]
Multiply 3 and 5.
[tex]l = 15 - 5[/tex]
Subtract 5
[tex]l = 10[/tex]
Therefore the width is 5 and the length is 10.
