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kjhgfd

  • 3 years ago

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

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  1. tjones89
    • 3 years ago
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    Do you know the equation for the perimeter of a rectangle?

  2. tjones89
    • 3 years ago
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    |dw:1350324998775:dw|

  3. tjones89
    • 3 years ago
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    There are four sides, so to find the perimeter we just add them all up\[perimeter = length + length + width + width\]

  4. tjones89
    • 3 years ago
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    we can simplify this expression by using multiplication because \[width + width = 2 \times width\]

  5. tjones89
    • 3 years ago
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    and \[length + length = 2 \times length\]

  6. tjones89
    • 3 years ago
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    so the perimeter equation looks like this\[perimeter = 2 \times length + 2 \times width\]

  7. tjones89
    • 3 years ago
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    this problem gives us two pieces of information that we can insert into out equation for perimeter

  8. tjones89
    • 3 years ago
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    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 \[length = width + 4\]

  9. tjones89
    • 3 years ago
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    we can substitute both of these pieces of information into the equation for perimeter\[perimeter = 2 \times length + 2 \times width\]

  10. tjones89
    • 3 years ago
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    to get:\[50 = 2 \times (width + 4) + 2 \times width\]

  11. tjones89
    • 3 years ago
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    By substituting length with width + 4 we reduced the equation to a single variabale which we can solve.

  12. kjhgfd
    • 3 years ago
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    thanks

  13. tjones89
    • 3 years ago
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    can you handle it from here?

  14. kjhgfd
    • 3 years ago
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    yeah I had after the first two messages, but thanks for being so detailed I appreciate it

  15. kjhgfd
    • 3 years ago
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    Now how do I give you a medal?

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