Question 156649
Hi, Hope I can help,
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the perimeter of a rectangle is 60 inches and the length is 4 inches longer than the width. Find the dimensions of the triangle.(I think you mean "Find the dimensions of the rectangle)
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The perimeter is all the sides added together, in this case there are 4 sides
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We need to assign variables to the length and width .
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the length is 4 inches longer than the width. ( we can say that the width is "x" ), if the length is 4 inches longer than the width, the length = "x+4"
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Length = "x+4"
Width = "x"
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Our Perimeter = 60, Perimeter of Rectangle = {{{ 2(Length) + 2(Width) }}} = {{{ 2(L) + 2(W) }}}, we can replace "L" and "W" with the length and width variables
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(since we already have our perimeter, "60", we can say {{{ 2(L) + 2(W) = 60 }}} )
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Let's replace "L" with "x+4", "W" with "x",(since we already have our perimeter, "60", we can say {{{ 2(L) + 2(W) = 60 }}}
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{{{ 2(L) + 2(W) = 60 }}} = {{{ 2(x+4) + 2(x) = 60 }}}
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We will use distribution
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{{{ 2(x+4) + 2(x) = 60 }}} = {{{ cartoon ( 2(x+4) + 2(x)= 60, highlight (2)(highlight(x)+4) + 2x = 60, highlight(2)(x+highlight(4)) + 2x = 60, 2x + 8 + 2x = 60) }}}
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{{{ 2x + 8 + 2x = 60 }}}
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Now let us rearrange the numbers
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{{{ 2x + 8 + 2x = 60 }}} = {{{ 2x + 2x + 8 = 60 }}}
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We will now add like terms {{{ cartoon ( highlight(2x) + highlight(2x) + 8 = 60, 4x + 8 = 60) }}}
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{{{ 4x + 8 = 60 }}}
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Now lets move the "8" to the right side
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{{{ cartoon ( 4x + 8 = 60, 4x + 8 -8 = 60 -8, 4x = 60-8, 4x = 52) }}}
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{{{ 4x = 52 }}}
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Now lets divide each side by "4" to find "x"
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{{{ cartoon ( 4x = 52, 4x/4 = 52/4, highlight(4)x/highlight (4) = 52/4, cross(4)x/cross(4)=52/4,x = 52/4,x = 13 ) }}}
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{{{ x = 13 }}}
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Just replace "x" with 13 in our length and width variables
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Length = "x+4" = "13+4" = "17"
Width = "x" = "13"
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Length = "17"
Width = "13"
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We can check by replacing "L"(Length) with "17", "W"(Width) with "13" in our equation, or by replacing "x" with "13" in one of the other equations
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{{{ 2(L) + 2(W) = 60 }}} = {{{ 2(17) + 2(13) = 60 }}} = {{{ 34 + 26 = 60 }}} = {{{ 60 = 60 }}} (True)
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Or we can check this way, by replacing "x" with "13"
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{{{ 2(x+4) + 2(x) = 60 }}} = {{{ 2(13+4) + 2(13) = 60 }}} = {{{ 2(17) + 2(13) = 60 }}} = {{{ 2(17) + 2(13) = 60 }}} = {{{ 34 + 26 = 60 }}} = {{{ 60 = 60 }}}
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the length(17) is 4 inches longer than the width(13) "True"
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Length = "17 inches"
Width = "13 inches"
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Hope I helped, Levi