Algebra is one of the important aspects of  Mathematics. It helps us make connections between different things, to express them using equations, and to see how they will work out. And because Algebra is an integral part of Maths, you need to know how to solve such problems successfully.

Consider the diagram shown below, which together with the steps that follow have been provided by BBC Bitesize


The length of the rectangle is Equation: 2x + 5, and the width of the rectangle is Equation: 3x - 2.  The perimeter of the rectangle is 46 cm. Find the value of Equation: x

1. What Do I Have To Do?

Read the question through twice. Highlight or underline the important pieces of information in the question as done above.

2. What Information Do I Need?

The highlighted words are the most important ones. The key word in the question is perimeter. The question asks to find the value of Equation: x. The answer might be a whole number (1, 2, 10, 1000), a fraction (1/2, 5/6, 37/168) or decimal (0.5, 0.83, 0.22) .

3. What Information Don’t I Need?

Everything in this question is relevant to working out the answer.

4. What Maths Can I Do?

Step A

Opposite sides in a rectangle are equal. Hence, the two longer sides (length), and two shorter sides (breadth) are the same.

perimeter of rectangle

Step B

The perimeter of a shape is found by adding up all the sides. Find an expression for the perimeter:

Equation: 2x + 5 + 3x - 2 + 2x + 5 + 3x - 2 = 10x + 6

Step C

The perimeter of the rectangle is 46 cm, therefore:

Equation: 10x + 6 = 46

Step D

Solve this equation to find Equation: x:

Equation: 10x + 6 = 46

Start by subtracting 6 from both sides:

Equation: 10x = 40

Divide both sides by 10:

Equation: x = 4

5. Is My Solution Correct?

Check the answer by substituting the value of Equation: x into the length and width.

The length of the rectangle is: Equation: 2x + 5

If Equation: x = 4 then Equation: 2 times 4 + 5 = 13:text{cm}.

The width of the rectangle is: Equation: 3x - 2

If Equation: x = 4 then Equation: 3 times 4 - 2 = 10:text{cm}.

Add up these figures to see if they will give you 46:

Equation: 13 + 10 + 13 + 10 = 46

6. Have I Completed Everything?

The question asks for the value of Equation: x, this has been found and checked.

Nothing else was asked for.

And there, you have successfully completed a simple algebraic problem!