Step 1:
For a rectangle, we know that opposite sides are equal
Hence we use this information to draw a rectangle and label the 4 sides.
Step 2:
We know that the perimeter of a rectangle is equal to the sum of the length of the 4 sides.
This is equal to 2 x length + 2 x width
Hence we write the following equation:
2*(2x+4) + 2*(3x-2) = Perimeter
2*(2x+4) + 2*(3x-2) = 54
Step 3:
Now we have to solve the above equation in terms of x:
2*(2x+4) + 2*(3x-2) = 54
Now using BIDMAS, we notice that we can't perform any operation in the brackets first, as we have x which is an unknown term, hence we proceed by multiplying out each of the brackets.
We get,
4x+8+6x-4 = 54
Now we proceed by adding the common terms on the LHS
This means we add 4x to 6x and subtract 4 from 8.
10x+4= 54
The next step is subtract 4 from each side, as this means will be left only with are unknown term on the LHS
10x=50
The final step is to divide both sides by 10:
x=5
Hence the value of x we have been looking for is 5.
Step 4:
Now we have to check if the value of x we have found above is correct:
As mentioned above, the sum of the length of the 4 sides of the rectangle are equal to the perimeter:
Adding all the sides together we get:
4x+8+6x-4 = 54
which is equal to:
10x+4= 54
as seen from above.
Now substituting x by 5, we get:
10*(5) + 4 = 50 + 4 = 54 using BIDMAS
Hence we have showed that LHS=RHS and hence we have verified that our answer is correct.