Question

Can you help with a geometry problem? Perimeter of a rectangle is 64 and the width is 6 centimeters less than the length, so what’s the width

Answer 1

For this problem, we are given the perimeter of a rectangle and a relation between the width and the length. We need to determine the width.

The perimeter of a rectangle is given by:

`P=2(\text{ width + length\rparen}`

Therefore, we have:

`2\text{ width}+2\text{ length}=64`

We know that the width is 6 centimeters less than the length, therefore we can write the expression below:

`\text{ width}=\text{ length}-6`

If we replace the expression above on the second one, we have:

`\begin{gathered} 2(\text{ length}-6)+2\text{ length}=64\\ \\ 2\text{ length}-12+2\text{ length}=64\\ \\ 4\text{ length}=64+12\\ \\ 4\text{ length}=76\\ \\ \text{ length}=(76)/(4)=19 \end{gathered}`

We can use this value to find the width, which is:

`\text{ width}=19-6=13`

The width is equal to 13 cm.