Question 978890: a rectangular garden is 30 feet by 40 feet long.A walk of uniform with that surrounds it has an area of 280 square feet.Find the width of the walk
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A rectangular garden is 30 feet by 40 feet long.
A walk of uniform width that surrounds it has an area of 280 square feet.
Find the width of the walk.
:
Find the total area including the garden and walkway
(30*40) + 280 = 1480 sq/ft
:
Let x = the width of the walkway, the walkway adds 2x to the length and width of the garden
:
Overall area equation
(2x+40)*(2x+30) = 1480
FOIL
4x^2 + 60x + 80x + 1200 = 1480
4x^2 + 140x + 1200 - 1480 = 0
4x^2 + 140x - 280 = 0
Simplify, divide by 4
x^2 + 35x - 70 = 0
This won't factor, use the quadratic equation, a=1; b=35; c=-70
Two solutions but only one makes sense
x = 1.9 ft is the width of the walkway
:
;
Confirm our solution by finding the area including the walkway
(3.8+30)*(3.8+40) = 1480.44 close enough
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