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43 votes
43 votes
The length of the longer side of a rectangle is 2 in. less than twice the length of

the shorter side. The area of the rectangle is 60 in2. What is the difference
between the lengths of the longer and shorter sides?

User Justqb
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1 Answer

23 votes
23 votes
Here, this question is about extracting information from the text: the only thing you need to know in advance is the formula for area of a rectangle which is length times width equals area ( l x w = a).

To unpack the words, here is a list of what we are told:

The length is given to us as a function of width which means if I’m selecting something to be “x,” my variable I’m going to make it the width. Thus first things first - “x” will equal my width. Remember though that when we solve this equation we are building it will give us the LENGTH

We are told “2 feet more than.” “More than sounds a lot like addition doesn’t it? Therefore somewhere in my equation I’m adding two to something!

We are told “Twice the width.” Twice sounds a lot like multiplication doesn’t it? Therefore, somewhere in my equation I’m multiplying something by 2!

Finally we are told that the area is 60 square feet! This means what? That l x w = 60! This means that whatever I do in my equation, after the equals sign will be “60l”

Okay! Time to build the equation!
First… it’s equal to 60 so it begins with … = 60
Next, the first thing we said is the width would be x so since we are using l x w = a, I can put in x for the width so… l * x = 60

Now the tricky part…how is the length defined? Well we know! It’s 2 times the width plus 2! So…this is what the whole thing looks like: (2x+2)x = 60

Now we solve:
Distribute the x to eliminate the parentheses: 3x + 2x = 60

Combine like terms: 5x = 60

Divid both sides by 5: x = 12

REMEMBER THAT X IS ONLY THE LENGTH!
So the width is 12 minus two divided by 2 or 5

So Length = 12, Width = 5

check it: l x w = A, 12 x 5 = 60

Done
User DtotheG
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3.0k points