SOLUTION: a rectangular flower garden is surrounded by walkway 4 meters wide.The flower garden is 6 meters longer than it is wide. if the area of only he gardenia 137 square meters less than

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Question 1111488: a rectangular flower garden is surrounded by walkway 4 meters wide.The flower garden is 6 meters longer than it is wide. if the area of only he gardenia 137 square meters less than twice the area of only the walkway, find the dimensions of the entire plot
Answer by mananth(16946) About Me  (Show Source):
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a rectangular flower garden is surrounded by walkway 4 meters wide.The flower garden is 6 meters longer than it is wide. if the area of only he gardenia 137 square meters less than twice the area of only the walkway, find the dimensions
let width of garden be x
length will be x+6
area of garden = x(x+6)
area of plot = (x+8)(x+14)
As per the condition
area of garden =2(area of walkway)-137
Area of walkway =((x+8)(x+14)-x(x+6))
area of garden = 2((x+8)(x+14)-x(x+6))-137
x%28x%2B6%29=+2%28x%5E2%2B22x%2B112-x%5E2-6x%29-137
x%5E2%2B6x+=+2%2816x%2B112%29-137
x%5E2%2B6x+=+32x%2B224-137
x%5E2-26x-87=0
x%5E2-29x%2B3x-87=0
x(x-29)+3(x-29)=0
(x+3)(x-29)=0
x=29 width of garden
length = 29+6 =35
width of plot = 29+8=37
length of plot = 35+8 =43
Area of plot = 43*37 = 1591 m^2
CHECK
area of garden = 35*29=1015
area of plot = 1591 m^2
area of walk way = 576 m^2