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The perimeter of a rectangle is 96 inches. If the length of the rectangle is six less than five times the width, what is the length of the rectangle?

 Sep 2, 2021
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The primary focus of a word problem is teaching you how to turn words into systems of equations, so I'm only going to do that, and if you need furthrer help with the problem, simply ask for the answer and I will follow up with the steps to it.

 

The first sentence names the perimiter of the rectangle. Let's make a variable for it, P. We're also provided the value of 96 inches. Let's make add this o the system.

 

P = 96

 

The second part of the sentence names a relationship between length and width, so let's add variables for those, and call them l and w. We also get the relationship between these two:

 

l (the length) = 5w ("five times the width") - 6 ("six less than")

 

This doesn't help us on its own, but there's a third equation that's implied within the problem. The word that tells us is the word rectangle. It doesn't help on its own, but it helps when it adds the relationship between the constant within the problem, and the other relationship between length and width.

 

Rectangles have the property of their perimeters being twice the sum of their length and height. In equations, for a rectangle:

 

= 2*(l + w)

 

Think you can take it from here?

 Sep 2, 2021
edited by helperid1839321  Sep 2, 2021

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