Question

Are there other rectangles that have an area of 8 cm2 but have different dimensions than the one shown? Explain how you know. Hint: What are the factors of 8?

Answer 1

Remember that the formula of the area of a rectangle is

`A=lw`

Where l is the length and w is the width.

Then, we need to find all the possible pairs of numbers l and w such that

`\begin{gathered} A=8 \\ \Rightarrow lw=8 \end{gathered}`

The case given by the problem is 2*4=8 but there are many more, for example

`\begin{gathered} l=1 \\ \Rightarrow1\cdot w=8 \\ \Rightarrow w=8 \\ \Rightarrow(l,w)=(1,8) \end{gathered}`

Or even

`\begin{gathered} l=3 \\ \Rightarrow3w=8 \\ \Rightarrow w=(8)/(3)=2.6666\ldots \end{gathered}`

There are infinite rectangles with areas equal to 8cm^2