(GCSE) A rectangle has the following characteristics: its length is (2x + 5), its width is (3x - 2). The perimeter of the rectangle is 46 cm. What is the value of x?
First of all draw the rectangle, name its sides and annotate its characteristics.
Define the data you have and what you are looking for.
Write down the general formula for the perimeter of a rectangle: p = a + a + b + b (where e.g. "a" is the width and "b" is the length).
Set an expression with the data you have: 46 = (3x - 2) + (3x - 2) + (2x + 5) + (2x + 5). Sum up the variables and the numbers in the expression. Group the variables to the left of the "=" sign and numbers to the right, remembering that the members of the expression that change their original position will also change their sign.
You should end up with x = 4.
You can check your answer by substituing x = 4 in the expression you set up. If you get 46 by solving the right side of the expression, then your solution is the right one.
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