Forming and simplifying equations
Usually, when we are asked to form an equation, it is based on some knowledge of area, perimeter or angles. You will have to make sure that you have a good understanding of these topic areas in order to attempt these questions, so it is a good idea to revise them together.
Example
Write and simplify an expression for the perimeter of the shape below.
Solution
To calculate perimeter you simply add up all of the sides. This will give the result:
\({x}\) + 7 + \({x}\) + 10 + \({x}\) + 4
We can then simplify this expression to give: 3\({x}\) + 21
Subsequent questions may then involve being given a value for the perimeter and having to solve for \({x}\). Let’s look at how that would work.
Example
The perimeter for the above shape is measured to be 33 cm. Calculate the value of \({x}\).
Solution
Setting our expression equal to 33 gives 3\({x}\) + 21 = 33
Subtracting 21 from both sides: 3\({x}\) = 33 – 21 = 12
Dividing both sides of the equation by 3: \({x}\) = 4 cm
Question
Write a simplified expression for the area of the following triangle.
As this question is asking for an expression for area we need to recall how to calculate the area of a triangle.
The area of a triangle is calculated using the equation \(\text {area =}~\frac {base \times height} {2}\)
Substituting our base and height into the equation:
\(\text {area =}~\frac{(x~–~3)\times{8}}{2}\)
Expanding the bracket:
\(\text {area =}~\frac{8x~–~24}{2}\)
Simplifying:
\(\text {area =}~{4x~–~12}\)
More guides on this topic
- Equations of lines – WJEC
- Equations of curves - Intermediate & Higher tier – WJEC
- Basic algebra – WJEC
- Factorising - Intermediate & Higher tier – WJEC
- Quadratic expressions - Intermediate & Higher tier – WJEC
- Sequences – WJEC
- Functions - Higher only – WJEC
- Inequalities - Intermediate & Higher tier – WJEC
- Simultaneous equations - Intermediate & Higher tier – WJEC