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The length of a rectangle is five centimetres greater than its width.
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If the width is fifty-two centimetres, what is its perimeter?
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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.
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Now we tend to call the longer side the length and the shorter side the width.
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Well, doesn’t really matter.
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Now in our case, the length of the rectangle is five centimetres greater than its width.
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And we’re told that the width is fifty-two centimetres.
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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.
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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.
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Now we’ve been asked to find the length of the perimeter, and that involves adding up all of the side lengths.
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So it’s this distance here plus this distance here plus this distance here plus this distance here.
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So that’s fifty-two centimetres plus fifty-seven centimetres plus fifty-two centimetres plus fifty-seven centimetres.
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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.
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Now in fact, we can rearrange that like this using the distributive property.
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So two times fifty-two plus two times fifty-seven is the same as two times fifty-two plus fifty-seven.
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Because to evaluate that, I would just do two times fifty-two plus two times fifty-seven.
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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.
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Now perimeter is a length, and the length units that were given in the question were centimetres.
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So we can give our answer as two hundred and eighteen centimetres.
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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.
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At least you can get some credit for knowing how to do the right things even if you put the wrong numbers somewhere.