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?

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Answer 1 · 2018-06-17T15:52:12

Width is 6 meters and length is 7 meters.

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:

$y=2x-5$

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

$P=2x+2y$
$26=2(x+y)$

$x+y=13$

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

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

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

$y=2(6)-5$
$y=7$

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