Question 153085
Hi, Hope I can help,
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The length of a rectangle is 6 more feet than twice the width. If the perimeter is 24 ft., what are the dimensions?
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First, we have to find out the variables, The length of a rectangle is 6 more feet than twice the width. If the perimeter is 24 ft., what are the dimensions?
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We see that the width is "x", the length is 6 more feet than twice the width, or "2x + 6", now we will place the variables into a formula
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the Perimeter formula for a rectangle = {{{ 2(length) + 2(width) = Perimeter }}}
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{{{ 2(L) + 2(W) = Perimeter }}}
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We can replace the width and length into the formula, our Perimeter = 24 feet
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{{{ 2(L) + 2(W) = Perimeter }}} = {{{ 2(2x + 6) + 2(x) = 24 }}}
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We will use distribution
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{{{ 2(2x + 6) + 2(x) = 24 }}} = {{{ 4x + 12 + 2x = 24 }}}
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We will add like terms
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{{{ 4x + 12 + 2x = 24 }}} = {{{ 4x + 2x + 12 = 24 }}} = {{{ 6x + 12 = 24 }}}
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We will move the "12" over to the right side
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{{{ 6x + 12 - 12 = 24 - 12 }}} = {{{ 6x = 12 }}}
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We will divide each side by "6"
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{{{ 6x/6 = 12/6 }}}
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{{{ x = 2 }}}
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x = 2
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We now know the width, since the width = "x"
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width = "x", or "2"
length = (2x+6), or (2(2) + 6), or (4+6), or "10"
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width = "2" feet
length = "10" feet
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"10" is 6 more feet than twice the width(2)
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We can check by replacing "x" in our equation ( x = 2)
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{{{ 2(2x + 6) + 2(x) = 24 }}} = {{{ 2(2(2) + 6) + 2(2) = 24 }}}
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{{{ 2(2(2) + 6) + 2(2) = 24 }}} = {{{ 2(4 + 6) + 2(2) = 24 }}}
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{{{ 2(4 + 6) + 2(2) = 24 }}} = {{{ 2(10) + 2(2) = 24 }}}
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{{{ 2(10) + 2(2) = 24 }}} = {{{ 20 + 4 = 24 }}}
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{{{ 20 + 4 = 24 }}} = {{{ 24 = 24 }}} (True)
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Length = 10 feet
Width = 2 feet
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Hope I helped, Levi