Solve the problem.
-The perimeter of a rectangular room is 174 feet. Find the length and width of the room if the length is 9 feet longer than twice the width.
A) w = 31 ft; l = 71 ft
B) w = 52 ft; l = 122 ft
C) w = 26 ft; l = 61 ft
D) w = 39 ft; l = 48 ft

Question

Quizplus · Accepted Answer

Let's call the width of the room "w" and the length "l". We can set up two equations based on the given information:
Perimeter = 2(length + width)
174 = 2(l + w)
l = 9 + 2w  (since "the length is 9 feet longer than twice the width")
Now we can substitute the second equation into the first equation and solve for w:
174 = 2(9 + 3w)
87 = 9 + 3w
78 = 3w
w = 26
To find the length, we can plug in w = 26 to the equation l = 9 + 2w:
l = 9 + 2(26)
l = 61
Therefore, the width is 26 feet and the length is 61 feet, making choice C the best answer. Let w be the width of the room.
Then the length of the room is 2w+9.
The perimeter of the room is 2(length + width) = 2(2w+9 + w) = 6w+18.
So we have the equation 6w+18 = 174.
Solving for w, we get w = 26.
So the width of the room is 26 feet, and the length is 2w+9 = 2(26)+9 = 61 feet.
Therefore, the answer is C, w = 26 ft; l = 61 ft.

Solve the Problem. -The Perimeter of a Rectangular Room Is 174 Feet. Find