Final answer:
To find the dimensions of the rectangle, we can set up two equations based on the given information: the perimeter equation and the equation for the relationship between the length and width. Solving this system of equations, we find that the dimensions of the rectangle are Length = 35 inches and Width = 10 inches.
Step-by-step explanation:
To solve this problem, we can set up two equations based on the given information. Let's denote the length as 'L' and the width as 'W'. The perimeter of a rectangle is given by the formula 2(L + W), so we can write the equation 2(L + W) = 90. Also, we are told that the length is 5 inches less than 4 times the width, so we can write the equation L = 4W - 5.
Now, we can solve this system of equations. Substituting the second equation into the first equation, we get 2((4W - 5) + W) = 90. Simplifying the equation, we have 10W - 10 = 90. Adding 10 to both sides and then dividing by 10, we find W = 10. Substituting this value back into the second equation, we have L = 4(10) - 5 = 35.
Therefore, the dimensions of the rectangle are Length = 35 inches and Width = 10 inches.