The length of a rectangle is four more than triple the width. If the perimeter is 120 inches, find the dimensions
Let's assume the width of the rectangle is x inches.
According to the problem, the length of the rectangle is four more than triple the width, which can be expressed as 3x + 4 inches.
The formula for the perimeter of a rectangle is P = 2(l + w), where P is the perimeter, l is the length, and w is the width.
Given that the perimeter is 120 inches, we can write the equation as 120 = 2((3x + 4) + x).
Simplifying the equation, we have 120 = 2(4x + 4).
Distributing 2 to the terms inside the parentheses, we get 120 = 8x + 8.
Subtracting 8 from both sides of the equation, we have 120 - 8 = 8x.
Simplifying further, we get 112 = 8x.
Dividing both sides of the equation by 8, we get 112/8 = x.
Solving for x, we find that x = 14.
Therefore, the width of the rectangle is 14 inches.
The length of the rectangle is three times the width plus four, which is 3(14) + 4 = 42 + 4 = 46 inches.
Therefore, the dimensions of the rectangle are 46 inches by 14 inches.