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

Algebra.Com
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)   (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.

RELATED QUESTIONS

If one side of a square is increased by 8 cm and an adjacent side is decreased by 2 cm, a (answered by jrfrunner)
If one side of a square is increased by 8 cm and an adjacent side decreased by 2 cm, a... (answered by J2R2R)
If one side of a square is increased by 8 cm and an adjacent side decreased by 2 cm a... (answered by mananth)
A quadrilateral with one pair of opposite sides parallel is a __________. parallelogram, (answered by MathLover1)
A rectangle having twice the area of a square is formed by decreasing two parallel sides... (answered by jojo14344)
i need help to understand and solve these 5 problems, thank u 1.the quadrilateral... (answered by stanbon)
A box with a rectangular base and no top is formed by cutting squares out of the corners (answered by josgarithmetic)
If two opposite sides of a square are increased by 9 meters and the other sides are... (answered by edjones)
If two opposite sides of a square are increased by 15 meters and the other sides are... (answered by jim_thompson5910)