Question

jackson likes to go running around the perimeters of two fields near his home. the two fields have side dimensions as shown in the diagrams. if the perimeter of rectangle a is ( f(x) ) and the perimeter of rectangle b is ( g(x) ), which function represents the difference, ( h(x) ), in the perimeters of the rectangles? ( h(x)=0.5 x^{2}-3 x ) ( h(x)=-x + 2 ) ( h(x)=x + 6 ) ( h(x)=-x - 6 )

Explanation:

Step1: Calculate the perimeter of rectangle A

The formula for the perimeter of a rectangle is \(P = 2(l + w)\). For rectangle A, \(l = 2x\) and \(w=x - 1\).

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Step2: Calculate the perimeter of rectangle B

For rectangle B, \(l = 3x + 2\) and \(w = 0.5x\).

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Step3: Calculate the difference \(h(x)=f(x)-g(x)\)

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Answer:

\(h(x)=-x - 6\)