SOLUTION: A square poster is replaced by a rectangular poster that is 2 inches wider and 2 inches shorter. What is the difference in the number of square inches between the area of the large
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Question 1199408: A square poster is replaced by a rectangular poster that is 2 inches wider and 2 inches shorter. What is the difference in the number of square inches between the area of the larger poster and the smaller poster? Answer by math_tutor2020(3838) (Show Source):
The rectangular poster is 2 inches wider.
This means x becomes x+2 along the width.
Meanwhile, the height goes from x to x-2 because it's 2 inches shorter.
The square poster is x inches by x inches.
The rectangular poster is (x+2) inches by (x-2) inches.
A = area of the square = side*side = x*x = x^2
B = area of the rectangle = width*height = (x+2)(x-2) = x^2-4
Use the difference of squares rule to see why (x+2)(x-2) = x^2-4.
In short
A = x^2
B = x^2-4
Subtract these items to find that
A - B = (x^2) - (x^2-4) = x^2-x^2+4 = 4
So
A-B = 4
The difference in area is 4 square inches.
The square has the larger area because we subtracted off 4 in the area of the rectangle.
Put another way:
A = area of the square = x^2
B = area of the rectangle = x^2-4 = A-4
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