gabbyalicorn
  • gabbyalicorn
The width of a rectangle is 6 in. less than its length. The perimeter is 68 in. What is the width of the rectangle? in.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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gabbyalicorn
  • gabbyalicorn
Hi pooja.
pooja195
  • pooja195
Uh i think the answer is in the question....if im right
anonymous
  • anonymous
divide it in two first

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Jhannybean
  • Jhannybean
|dw:1442028600183:dw|
Jhannybean
  • Jhannybean
Omg I forgot the shapes have the "fill" option.... anyway.
anonymous
  • anonymous
yeah
gabbyalicorn
  • gabbyalicorn
When you say divide two first, do you mean 68 ÷ 2 and 6÷ 2
anonymous
  • anonymous
no 68 by 2
anonymous
  • anonymous
then subtract 6 from that
gabbyalicorn
  • gabbyalicorn
okay, that is 34...
Jhannybean
  • Jhannybean
the length of the rectangle is given, but they say the `width` `is (equal to)` the `length - 6 in`You can rewrite this as \(\sf w = L-6\)
Jhannybean
  • Jhannybean
So the Perimeter of a rectangle is represented as: \[\sf P = 2L +2W\]
Jhannybean
  • Jhannybean
Since we're given the perimeter, and that is = 68 in. we can substitute that in to our formula. \[\sf 68 = 2L +2W\]
Jhannybean
  • Jhannybean
But we also know something else, \(\sf W=L-6\)
gabbyalicorn
  • gabbyalicorn
68 - 6?
Jhannybean
  • Jhannybean
So we can substitute this in to the formula for the perimeter. \[\sf 68 = 2L+2(L-6)\]
Jhannybean
  • Jhannybean
Are you following, @gabbyalicorn ?
gabbyalicorn
  • gabbyalicorn
Um, somewhat... I don't really get it but i'm following the steps if that's what you mean. :)
Jhannybean
  • Jhannybean
Which part are you confused with? Let's clarify that before moving on.
gabbyalicorn
  • gabbyalicorn
is L the variable we are trying to find
gabbyalicorn
  • gabbyalicorn
the number for...
Jhannybean
  • Jhannybean
We are trying to find W (width). The problem indiscreetly gives us the equation for the width by saying that the width IS 6 LESS THAN the length. We can write an equation for that. \(\sf w = L-6\)
gabbyalicorn
  • gabbyalicorn
but what is L
Jhannybean
  • Jhannybean
But we can't automatically find the width, \(\sf w\) can we? We need to find the length, \(\sf L\) first.
Jhannybean
  • Jhannybean
That is where we use the equation for the perimeter of the rectangle. \(\sf P = 2L +2w\)
Jhannybean
  • Jhannybean
Do you see how this works?
gabbyalicorn
  • gabbyalicorn
I think I'm getting it...
Jhannybean
  • Jhannybean
Okay, so we have \[\sf 68 = 2L+2(L-6)\] We need to first distribute (meaning multiply) 2 to each term inside the parenthesis. \[2 \cdot L =~?\]\[2\cdot (-6) =~?\]
gabbyalicorn
  • gabbyalicorn
|dw:1442029733818:dw|
Jhannybean
  • Jhannybean
Good
gabbyalicorn
  • gabbyalicorn
:)
Jhannybean
  • Jhannybean
\[\sf 68 = 2L +2L-12\]We add +12 to both sides of the equation.
gabbyalicorn
  • gabbyalicorn
why - 12 I thought you said add
Jhannybean
  • Jhannybean
because we want to isolate the L's to one side of the equation, we need to eliminate the 12 from that side. In order to eliminate it we need to add +12 to it. \[\sf +12-12 = 0\]So, \(\sf 68 + 12 =~?\)
gabbyalicorn
  • gabbyalicorn
80
Jhannybean
  • Jhannybean
So now we have \[\sf 80 = 2L + 2L\]\[\sf 2L + 2L =~?\]
gabbyalicorn
  • gabbyalicorn
4L ?
Jhannybean
  • Jhannybean
Good.
gabbyalicorn
  • gabbyalicorn
:}
Jhannybean
  • Jhannybean
\[\sf 80 = 4L\]Now we want to isolate the right side of the equation so we have JUST L. This is when we divide BOTH sides of the equation by 4. \[\sf \frac{80}{4}=~?\]
gabbyalicorn
  • gabbyalicorn
20
Jhannybean
  • Jhannybean
ALRIGHT! So now we have figured out \(\sf L\). \[\sf L=20\]Now we can go back to our equation for width and plug in L. \[\sfW=L-6\]So therefore what does W =?
Jhannybean
  • Jhannybean
Sorry, typo. \(\sf W=L-6\)*
gabbyalicorn
  • gabbyalicorn
20 - 6 = 14?
Jhannybean
  • Jhannybean
That's correct :)
gabbyalicorn
  • gabbyalicorn
Yes. :)
Jhannybean
  • Jhannybean
Great! You worked it out yourself :)
gabbyalicorn
  • gabbyalicorn
:D Thank you for helping me and not giving up on me! I reallu appreciate it. :)
Jhannybean
  • Jhannybean
No problem ^^

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