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 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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