Question

The length of a rectangle is four times the width. If the area of the rectangle is 196square inches, then find the length and width

Answer 1

Let the length of the rectangle be "l" and width be "w".

The length is 4 times the width, we can write:

`l=4w`

The area is given as 196. We know area of a rectangle is A = lw, where l is length and w is width. Thus, we can write:

`196=lw`

Substituting the first equation into the second, we can solve for w. The process is shown below:

`\begin{gathered} 196=lw \\ 196=(4w)w \\ 196=4w^2 \\ w^2=(196)/(4) \\ w^2=49 \\ w=\sqrt[]{49} \\ w=7 \end{gathered}`

Now, using the 1st equation, we can solve for the length, "l". Shown below:

`\begin{gathered} l=4w \\ l=4*7 \\ l=28 \end{gathered}`

Answer:

Length = 28 inches

Width = 7 inches