anonymous
  • anonymous
The perimeter of a rectangle is 50 cm and the length is 4 cm longer than the width. Write and solve the system of equations using the substitution method. A. width = 10 cm, length= 14 cm B. width = 10 1/2 cm, length= 14 1/2 cm C. width = 11 cm, length= 15 cm D. width = 23 cm, length= 27 cm
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
Do you know the equation for the perimeter of a rectangle?
anonymous
  • anonymous
|dw:1350324998775:dw|
anonymous
  • anonymous
There are four sides, so to find the perimeter we just add them all up\[perimeter = length + length + width + width\]

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anonymous
  • anonymous
we can simplify this expression by using multiplication because \[width + width = 2 \times width\]
anonymous
  • anonymous
and \[length + length = 2 \times length\]
anonymous
  • anonymous
so the perimeter equation looks like this\[perimeter = 2 \times length + 2 \times width\]
anonymous
  • anonymous
this problem gives us two pieces of information that we can insert into out equation for perimeter
anonymous
  • anonymous
we are told that the perimeter = 50 and that the length is 4 more than the width so we can write the length like this \[length = width + 4\]
anonymous
  • anonymous
we can substitute both of these pieces of information into the equation for perimeter\[perimeter = 2 \times length + 2 \times width\]
anonymous
  • anonymous
to get:\[50 = 2 \times (width + 4) + 2 \times width\]
anonymous
  • anonymous
By substituting length with width + 4 we reduced the equation to a single variabale which we can solve.
anonymous
  • anonymous
thanks
anonymous
  • anonymous
can you handle it from here?
anonymous
  • anonymous
yeah I had after the first two messages, but thanks for being so detailed I appreciate it
anonymous
  • anonymous
Now how do I give you a medal?

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