The length of a rectangle is 5 less than twice its width. The perimeter is 26 meters. How do you find the dimensions of the rectangle?

Jun 17, 2018

Width is 6 meters and length is 7 meters.

Explanation:

Let width be $x$ and length be $y$. We know that the length of the rectangle is 5 less than twice its width. This can be written as:

$y = 2 x - 5$

We also know that the perimeter of the rectangle is 26 meters. The perimeter is the sum of all sides: 2 widths + 2 lengths.

$P = 2 x + 2 y$
$26 = 2 \left(x + y\right)$

$x + y = 13$

We now have two equations which we can solve simultaneously. Substitute $y = 2 x - 5$ into the second equation: $x + y = 13$

$x + \left(2 x - 5\right) = 13$
$3 x = 18$
$x = 6$

Now that we have a value for $x$ (width), we can sub this value into the first equation to get $y$ (length).

$y = 2 \left(6\right) - 5$
$y = 7$

There are other methods you can use to solve simultaneous equations.
Hope this helps :)