Question

The length of a rectangle is 5 less than twice it’s width.The perimeter is 26 meters.Find the dimensions of the rectangle.

Answer 1

Let l be the symbol for length

Let w be the symbol for width

`l = 2w - 5`

Our first equation is built according to the given that the length is twice the width subtracted by 5

Our second equation is built on the definition of perimeter. A perimeter is the sum of all sides of a polygon. A rectangle has 4 sides (2 lengths and 2 widths)

So the perimeter of a rectangle is=l+l+w+w=2l+2w

`2l + 2w = 26`

This will be our second equation;

I can make a system of equations of 2 unknowns using my 2 equations;

`2l + 2w = 26`

`l -2w = - 5`

Add the two systems together by adding everything that is before the equal sign together and everything after it together.

`2l + l + 2w - 2w = 26 - 5`

`3l = 21`

`l = (21)/(3) = 7 \: meters`

To find the width substitute L=7 in any equation;

`l = 2w - 5`

`7 = 2w - 5`

`7 + 5 = 2w`

12=2w

w=12/2=6

The app is bugging, the width is 6 meters and the length is 7 meters