To solve this problem, we will use the formula for the area of a rectangle, which is equal to length times width. We are given that the area of the rectangle is 68 square inches and the length of the rectangle is 5 inches more than 3 times the width.
Let's denote the width of the rectangle as w. From the problem statement, we know that the length of the rectangle, l, is 3w + 5.
So we can set up the equation as follows:
l * w = 68
Substitute the expression for l into the equation:
(3w + 5) * w = 68
To solve this equation, we expand it, rearrange terms and solve for w:
3w² + 5w = 68
3w² + 5w - 68 = 0
We find the roots of this equation using the quadratic formula. The value of w that we obtain is -17/3. Note that a rectangle cannot have a negative width, so this solution has no practical meaning in this context.
Next, we substitute w = -17/3 into the equation for the length to find the length:
l = 3 * (-17/3) + 5
l = -12
Again, a rectangle cannot have a negative length. Therefore, the problem as stated does not have a solution in the domain of real numbers that makes sense in this context.
(If your question implied that width and length could be negative as valid values, then the solution would be: length = -12 inches and width = -17/3 inches.)