Answer: Let's begin by assigning variables to represent the dimensions of the room. Let's use "l" to represent the length and "w" to represent the width.
We know that the length of the room is 5 feet longer than twice the width, so we can write an equation:
l = 2w + 5
We also know that the perimeter of the room is 178 feet. The formula for the perimeter of a rectangle is:
perimeter = 2(length + width)
Substituting the equation we found for the length, we get:
178 = 2(2w+5 + w)
Simplifying, we can combine like terms and solve for w:
178 = 2(3w+5)
89 = 3w+5
84 = 3w
w = 28
Now that we know the width is 28 feet, we can use the equation for the length to find the length:
l = 2w+5 = 2(28)+5 = 61
Therefore, the dimensions of the room are 61 feet by 28 feet.
Explanation: