Algebra is a wonderful thing if you know how to use it correctly. One of its major advantages is that it allows you to work with things you don't know, be they lengths of sides, sizes of numbers or something entirely different.
The technique we will discuss today is how to create and solve an equation to find one of these things that we don't know.
Example A rectangle has sides of (4x + 1) cm and 3 cm. If it has a perimeter of 16cm2. Find the area of the rectangle.
This question is a perfect of example of using an equation to solve a problem. The thing that gives it away is that we are asked for something and part of our question is an unknown (x).
Step 1: Draw a diagram if possible (or you aren't given one)
Step 2: Create an expression for the thing you know.
In this question, we are given the perimeter. We know that perimeter is adding the sides together so let's do that with the algebra.
4x + 1 + 3 + 4x + 1 + 3
8x + 8
It's worth noting that I haven't made this into an equation. This is just because the question asks for an expression.
Step 3: Create an equation for the thing you know.
We have just worked out an expression for the perimeter and we know that the perimeter is equal to 16. This gives us the equation...
8x + 8 = 16
Step 4: Solve the equation:
We can just do this using our basic solving equations rules (do the same to both sides, do the opposite operation)
8x + 8 = 16
8x + 8 - 8 = 16 - 8
8x = 8
8x ÷ 8 = 16 ÷ 8
x = 1
Step 5: Answer the question that was asked.
In this question, we are asked to find the area. To do this we need to find the lengths of the sides and then multiply them together.
Remember that we just found that x = 1
Side 1: 4x + 1 -- 4(1) + 1 = 5 cm
Side 2: 3 cm
Therefore we can see that the area of this rectangle is 5 x 3 = 15 cm2