The perimeter of rectangle is 18 inches and its length is l and width is w.

Write the equation 1 by using perimeter formula of rectangle is .

Apply distributive property: .

To get the equation 2, substitute the value of in perimeter formula of rectangle .

Divide each side by 2.

Cancel common terms.

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The system of equations are .

Since the coefficient of the w - term in the above two equations is same, eliminate these terms by subtracting the equations.

Write the equations in column form and add the corresponding columns to eliminate w - variable.

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The resultant equation is and solve for w.

Multiply each side by negative 1.

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Substitute the value of in either of the original equations and solve for l.

The second equation: .

Subtract 12 from each side.

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Divide each side by 3.

Cancel common terms.

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The length of the original rectangle is 4 inches and its width is 6 inches.

The length of the new rectangle inches and its width inches.

(a). The length of the original rectangle is 4 inches and its width is 6 inches.

(b). The length of the new rectangle 12 inches and its width 12 inches.