If the length of a rectangular planting field is 10 km and the width is x+1 km, for what values of x would the area of the planting field be greater than the perimeter?

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Answer 1 · 2018-05-27T09:56:50

#color(blue)(x> 3/2)#

#"length"=10km#

#"width"=x+1km#

#"Area"=10xx(x+1)=10x+10#

Perimeter is the sum of all sides of the rectangle:

#Perimeter"=10+10+x+1+x+1=2x+22#

Area greater than perimeter:

#10x+10>2x+22#

Solving for #x#:

Subtract 10 from both sides:

#10x>2x+12#

Subtract #2x# from both sides:

#8x>12#

Divide both sides by 8:

#x>12/8#

#x>3/2#

For #x>3/2# the area is greater than the perimeter.