Answer:
the length of the rectangle is 185 inches.
Explanation:
Let's denote the width of the rectangle as "w" (in inches) and the length of the rectangle as "L" (in inches).
Given that the length is 13 inches less than 6 times its width, we can write this as an equation:
L = 6w - 13
We are also given that the area of the rectangle is 6105 square inches:
Area = Length × Width
6105 = L × w
Substitute the expression for "L" from the first equation into the area equation:
6105 = (6w - 13) × w
Now, let's solve for "w":
6105 = 6w^2 - 13w
6w^2 - 13w - 6105 = 0
To solve this quadratic equation, you can use the quadratic formula:
w = (-b ± √(b^2 - 4ac)) / 2a
For this equation, a = 6, b = -13, and c = -6105. Plugging in these values:
w = (-(-13) ± √((-13)^2 - 4 × 6 × (-6105))) / (2 × 6)
w = (13 ± √(169 + 146520)) / 12
w = (13 ± √146689) / 12
Since we're dealing with measurements, the width can't be negative. So, taking the positive root:
w = (13 + 383) / 12
w = 396 / 12
w = 33
Now that we have the width, we can use the equation for the length:
L = 6w - 13
L = 6 × 33 - 13
L = 198 - 13
L = 185