Question

In the diagram, all measurements are in centimetres. The lengths of the side of the quadrilateral are 2r+5, 2r, 4r-3 and r. Find an expression, in terms of r, for the perimeter of the quadrilateral. Give your expression in its simplest form.

Answer 1

The expression for the perimeter of the quadrilateral is
`(9r+2)` cm.

Explanation:

The lengths of the side of the quadrilateral are
`2r+5,\ \ 2r,\ \ 4r-3\ \ and\ \ r`.

Perimeter means the sum of all side lengths in any geometric figure.

If the perimeter is
`P`, then.....

`P=[(2r+5)+(2r)+(4r-3)+(r)]\ cm\\ \\ P=(2r+5+2r+4r-3+r)\ cm\\ \\ P=(9r+2)\ cm\ \ [combining\ like\ terms]`

So, the expression for the perimeter of the quadrilateral is
`(9r+2)` cm.

Answer 2

The perimeter is simply the sum of all sides so:

p=2r+5+2r+4r-3+r combine like terms...

p=9r+2