The length of a rectangular room is 5 feet more than 3 times the width. The perimeter of the
room is 62 feet. Find the dimensions of the room.
What do you think is the right answer?
y = 3x+5
2(x+y) = 62
To solve this problem, let's assume the width of the room is represented by 'w' feet.
Given that the length of the room is 5 feet more than 3 times the width, we can express the length as follows:
Length = 3w + 5
The perimeter of a rectangle is given by the equation:
Perimeter = 2(length + width)
Substituting the values we have, the equation becomes:
62 = 2((3w + 5) + w)
Now, let's solve for the width.
62 = 2(4w + 5)
31 = 4w + 5
26 = 4w
w = 6.5
So, the width of the room is 6.5 feet.
To find the length, substitute the value of the width back into the expression for length:
Length = 3w + 5
Length = 3(6.5) + 5
Length = 19.5 + 5
Length = 24.5
Therefore, the dimensions of the room are:
Width = 6.5 feet
Length = 24.5 feet
To find the dimensions of the room, we need to set up equations using the given information.
Let's assume the width of the rectangular room is 'w' feet.
According to the given information, the length of the room is 5 feet more than 3 times the width. So, the length can be represented as (3w + 5) feet.
The formula for the perimeter of a rectangle is P = 2(l + w), where P represents the perimeter, l represents the length, and w represents the width.
In our case, the perimeter of the room is given as 62 feet. So we can set up the equation as follows:
62 = 2((3w + 5) + w)
Now, let's solve this equation to find the value of the width (w) and subsequently the length (l):
62 = 2(4w + 5) [Simplifying the expression inside the brackets]
62 = 8w + 10 [Distributing the 2]
62 - 10 = 8w [Bringing the constant term to the other side]
52 = 8w [Simplifying the left side]
52/8 = w [Dividing both sides by 8]
6.5 = w [Simplifying the right side]
Now we have the width 'w' as 6.5 feet.
To find the length ('l'), we can substitute the value of the width into the expression for the length:
l = 3w + 5
l = 3(6.5) + 5
l = 19.5 + 5
l = 24.5
Therefore, the dimensions of the rectangular room are:
Width = 6.5 feet
Length = 24.5 feet