A rectangular room is 6 meters longer than it is wide, and its perimeter is 28 meters. Find the dimension of the room.
The length is:_____meters and the width is___meters.
L=10
W=4
perimeter of rec = 2(l+w)
l=6+w
2(6+w+w)=28
12+4w=28
w=4m
l=6+w=6+4=10m
My responde is 20
Well, it seems like we have a mathematical mystery on our hands! Let's solve it together, shall we?
Let's start by assigning variables to the dimensions of the room. Let's call the width "w" (in meters) and the length "l" (in meters).
According to the given information, the length is 6 meters longer than the width. So, we can express this relationship as:
l = w + 6
Now, let's move on to the perimeter of the room. The perimeter is the sum of all the sides, which in this case is:
2w + 2l = 28
Since we know that l = w + 6, we can substitute this into the equation:
2w + 2(w + 6) = 28
Now let's solve for w:
2w + 2w + 12 = 28
4w + 12 = 28
4w = 16
w = 4
Great! Now that we know the width is 4 meters, we can substitute this value back into one of the equations to find the length:
l = w + 6
l = 4 + 6
l = 10
So, the dimensions of the room are:
The length is 10 meters and the width is 4 meters.
To find the dimensions of the rectangular room, we need to set up an equation based on the given information.
Let's assume the width of the room is "x" meters.
According to the problem, the length of the room is 6 meters longer than the width, which means the length would be (x + 6) meters.
The perimeter of a rectangle is given by the formula: Perimeter = 2(length + width).
In this case, we are given that the perimeter is 28 meters.
So, we can set up the equation:
28 = 2((x + 6) + x)
Simplifying the equation:
28 = 2(2x + 6)
28 = 4x + 12
Subtracting 12 from both sides:
16 = 4x
Dividing both sides by 4:
4 = x
Therefore, the width of the room is 4 meters.
Now, we can substitute the value of x back into the equation for the length:
Length = x + 6
Length = 4 + 6
Length = 10 meters
So, the length of the room is 10 meters, and the width is 4 meters.