The length of a rectangle is five centimetres greater than its width. If the width is fifty-two centimetres, what is its perimeter? Now a rectangle is a quadrilateral that has four ninety-degree angles or four right
angles, and each pair of opposite sides are equal in length.
Now we tend to call the longer side the length and the shorter side the width. Well, doesn’t really matter. Now in our case, the length of the rectangle is five centimetres greater than its
width. And we’re told that the width is fifty-two centimetres. Now from these two things we can see that the length is the width plus five
centimetres that’s fifty-two plus five, which is fifty-seven centimetres.
Now since opposite sides are equal in length, this side must also be fifty-seven
centimetres and this side must also be fifty-two centimetres.
Now we’ve been asked to find the length of the perimeter, and that involves adding up
all of the side lengths. So it’s this distance here plus this distance here plus this distance here plus this
So that’s fifty-two centimetres plus fifty-seven centimetres plus fifty-two
centimetres plus fifty-seven centimetres. Or another way of writing that is because we had two sides that were fifty-two
centimetres and two sides that were fifty-seven centimetres, we can say that’s two
times fifty- two plus two times fifty-seven.
Now in fact, we can rearrange that like this using the distributive property. So two times fifty-two plus two times fifty-seven is the same as two times fifty-two
plus fifty-seven. Because to evaluate that, I would just do two times fifty-two plus two times
fifty-seven. Well now in this format, I can simply add fifty-two and fifty-seven,
which is a hundred and nine, and then do two times a hundred and nine, which is two
hundred and eighteen.
Now perimeter is a length, and the length units that were given in the question were
centimetres. So we can give our answer as two hundred and eighteen centimetres. It’s always a good idea to do a quick sketch to help organise your thoughts and also
to show the steps in your working out in case you make a small mathematical
error. At least you can get some credit for knowing how to do the right things even if you
put the wrong numbers somewhere.