Question

If the area of the rectangle is 20cm squared, then what is the width of the rectangle?

Answer 1

From the given diagram we get that:

$4x+2=10x-1.$

Subtracting 4x from the above equation we get:

$\begin{gathered} 4x+2-4x=10x-1-4x, \\ 2=6x-1. \end{gathered}$

Adding 1 to the above equation we get:

$\begin{gathered} 2+1=6x-1+1, \\ 3=6x\text{.} \end{gathered}$

Dividing the above equation by 6 we get:

$\begin{gathered} \frac{3}{6}=\frac{6x}{6}, \\ x=\frac{1}{2}\text{.} \end{gathered}$

Therefore, the length of the given rectangle is:

$10\cdot\frac{1}{2}-1=5-1=4\operatorname{cm}\text{.}$

Now, since the area of a rectangle is the length times the width, we can set the following equation:

$width\times4\operatorname{cm}=20cm^2\text{.}$

Dividing the above result by 4cm we get:

$\text{width}=5cm\text{.}$

Answer: The width of the given rectangle is 5cm.