Question

The length of a rectangle is 4 times its width.
The perimeter is 36.
Find the length and width of the rectangle.

Answer 1

Answer:

Length=14.4

Width=3.6

Step-by-step explanation:

l=4w

2l+2w=36

2(4w)+2w=36

8w+2w=36

10w=36

w=3.6

l=4w

4(3.6)

l=14.4

*check by plugging in answers into 2l+2w=36*

Answer 2

Answer:

$L=\frac{72}{5}$      or 14.4

$W=\frac{18}{5}$     or 3.6

Step-by-step explanation:

Please take note this probably not the easiest way to do the problem.

Formula for the Perimeter of Rectangle

$P=2L+2W$

We are given the perimter.

$36=2L+2W$

$L=4*W$

To solve I would use the Gauss-Jordan method. (it is advanced, but it makes sense to me)

$36=2L+2W$

$L=4*W$

Write the coefficients of each eqaution as rows in the matrix.

$\left[\begin{array}{ccc}2&2&36\\1&-4&0\\\end{array}\right]$

Divide the first row by 2.

$\left[\begin{array}{ccc}1&1&18\\1&-4&0\\\end{array}\right]$

Multiply row 1 by -1 and add it to row 2.

$\left[\begin{array}{ccc}1&1&18\\0&-5&-18\\\end{array}\right]$

Divide the second row by -5.

$\left[\begin{array}{ccc}1&1&18\\0&1&\frac{18}{5} \\\end{array}\right]$

Multiply row 2 by -1 and add it to row 1.

$\left[\begin{array}{ccc}1&0&\frac{72}{5} \\0&1&\frac{18}{5} \\\end{array}\right]$

We now have an augmented matrix.

$L=\frac{72}{5}$

$W=\frac{18}{5}$