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.
If we let the width be x m
and the length is 6 m more, wouldn't the length be x+6 m ?
remember perimeter is
twice the width + twice the length
take over.
To solve this problem, we can set up a system of equations based on the given information.
Let's assume that the width of the room is x meters. Given that the length is 6 meters longer than the width, we can express the length as (x + 6) meters.
The perimeter of a rectangle is calculated by adding the lengths of all its sides. In this case, the perimeter is given as 28 meters. Therefore, we can set up an equation as follows:
2(length + width) = perimeter
2((x + 6) + x) = 28
Simplifying the equation:
2(2x + 6) = 28
4x + 12 = 28
Now, let's solve for x by isolating it:
4x = 28 - 12
4x = 16
x = 16/4
x = 4
Therefore, the width of the room is 4 meters.
To find the length, we substitute the value of x back into the equation for length:
length = x + 6
length = 4 + 6
length = 10
So, the length of the room is 10 meters.
In conclusion, the dimension of the room is:
Length: 10 meters
Width: 4 meters