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.
Expand the multiplication
Subtract 50 from both sides.
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.
Plug in the solution to w.
Multiply 3 and 5.
Subtract 5
Therefore the width is 5 and the length is 10.
Expand the multiplication
Subtract 50 from both sides.
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.
Plug in the solution to w.
Multiply 3 and 5.
Subtract 5
Therefore the width is 5 and the length is 10.