Question

The perimeter of a rectangle is 38”. If the length is 3” morb than the width, find the width

Answer 1

To answer this question we will use the following formula for the perimeter of a rectangle:

$Perimeter=2(length+width).$

Since the perimeter of the rectangle is 38'' and the length is 3''' more than the width, then we can set the following system of equations:

$\begin{gathered} 38^{\prime}^^{\prime}=2(length+width), \\ length=width+3^{\prime}^{\prime}^{\prime}. \end{gathered}$

Substituting the second equation in the first one we get:

$38^{\prime\prime}=2(width+3^{\prime}^{\prime}^{\prime}+width).$

Simplifying the above result we get:

$\begin{gathered} 38^{\prime}^{\prime}=2(2width+3^{\prime}^{\prime}^{\prime}) \\ =4width+6^{\prime\prime\prime}. \end{gathered}$

We know that:

$1^{\prime}^{\prime}^{\prime}=\frac{1}{12}^{\prime}^{\prime}.$

Therefore:

$38^{\prime}^{\prime}^=4width+\frac{1}{2}^{\prime}^{\prime}.$

Subtracting 1/2'' from the above result we get:

$\begin{gathered} 38^{\prime}^{\prime}-\frac{1}{2}^{\prime}^{\prime}=4width+\frac{1}{2}^{\prime}^{\prime}-\frac{1}{2}^{\prime}^{\prime}, \\ 37\frac{1}{2}^{\prime}^{\prime}=4width. \end{gathered}$

Dividing the above result by 4 we get:

$9\frac{3}{8}^{\prime}^{\prime}=width.$