SOLUTION: Write an inequality then solve: A rectangle is formed from a given square by extending one pair of opposite sides 14 cm and the other pair 10cm. If the perimeter of the rectangle i

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Question 651007: Write an inequality then solve: A rectangle is formed from a given square by extending one pair of opposite sides 14 cm and the other pair 10cm. If the perimeter of the rectangle is at least twice the perimeter of the square, at most how long is a side of the square?
Answer by fcabanski(1391) About Me  (Show Source):
You can put this solution on YOUR website!
Call the sides of the square X. The perimeter is the sum of the sides, or 4X.


The rectangle's length is x+14 and width is x+10 (x extended the given lengths.) Its perimeter is 2L + 2W = 2(x+14) + 2(x+10) = 2x+28+2x+20 = 4x + 48.


The rectangle's perimeter (4x+48) is at least (meaning greater than or equal to) twice the perimeter of the square (2*4x).


4x+48 >= 8x Solve for x....subtract 4x from both sides.


48 >= 4x Divide both sides by 4: 12>=x.


x can be 12 or less.