Question 268890
The width of a rectangular playground is 2x -5 feet, and the length is 3x +9 feet. Write a polynomial P(x) that represents the perimeter and then evaluate this perimeter polynomial if x is 4 feet
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Ok so we know that the Perimeter of a rectangle is Width+Width+Length+Length
in equation form its {{{P=2W+2L}}} If W=2x-5 and L=3x+9 then we can find P(x)by using substitution
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{{{P=2W+2L}}}
{{{P(x)=2(2x-5)+2(3x-9)}}} multiply the 2 in to both sets of parenthasies
{{{P(x)=4x-10+6x-18}}} Add like terms
{{{P(x)=10x-28}}} this is your equation
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{{{P(x)=10x-28}}} If x=4 then solve for P(x)
{{{P(x)=10(4)-28}}}
{{{P(x)=40-28}}}
{{{P(x)=12}}} Perimeter = 12ft
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CHECKING ANSWER
{{{P(x)=2(2x-5)+2(3x-9)}}}
{{{12=2(2(4)-5)+2(3(4)-9)}}}
{{{12=2(8-5)+2(12-9)}}}
{{{12=2(3)+2(3)}}}
{{{12=6+6}}}
{{{12=12}}}
CORRECT