SOLUTION: a rectangular flower graden is surround 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 meter less than tw
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Question 1111490: a rectangular flower graden is surround 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 meter less than twice the area of only the walkway, find the dimensions of the entire plot
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
a rectangular flower graden is surround by walkway 4 meters wide.
The flower garden is 6 meters longer than it is wide.
if the area of only the garden: is 137 square meter less than twice the area of only the walkway, find the dimensions of the entire plot.
:
let w = the width of the garden
then
(w+6) = the length
and
w(w+6) = w^2 + 6w sq/m is the area of the garden
:
(w+8) = overall width
then
(w+14) the overall length
and
(w+8)(w+14) = w^2 + 15w + 8w + 112 = w^2 + 23w + 112 sq/m is the overall area
:
overall area - garden area = walkway area
w^2 + 22w + 112 - (w^2 + 6w) = 16w + 112 sq/m is the area of the walkway
:
"area of only the garden: is 137 square meter less than twice the area of only the walkway,"
garden area = twice walkway area - 137
w^2 + 6w = 2(16w+ 112) - 137
w^2 + 6w = 32w + 224 - 137
w^2 + 6w - 32w - 87 = 0
w^2 - 26w - 87 = 0
Factor
(w-29)(w+3) = 0
the positive solution
w = 29 meters is the width of the garden
and
29 + 6 = 35 meters is the length of the garden
therefore
29+8 = 37 meter is the overall width
and
35+8 = 43 meters is overall length
:
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