Question 978890
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