A rectangular garden, 42 feet by 20 feet, is surrounded by a walkway of uniform width. If the total area of the garden and walkway is 1248 square feet, what is the width of the walkway?
1 Answer
The width of the walkway is 3 feet.
Explanation:
Let's call the width of our walkway
Now, we can use the FOIL method to find an expression for the total area of the walkway and path in terms of
#(2x + 20)(2x + 42)#
#= 2x*2x + 2x*42 + 2x*20 + 20*42#
#= 4x^2 + 84x + 40x + 840#
#= 4x^2 + 124x + 840#
Finally, we know that this area must also be equal to 1248, so we can set these two expression equal and then solve for
#1248 = 4x^2 + 124x + 840#
#0 = 4x^2 + 124x - 408#
#0 = x^2 + 31x - 102#
This can be factored, since
#0 = (x - 3)(x + 34)#
By the properties of 0 and multiplication, this gives us these two equations, either of which could be true.
#(x-3) = 0 " " or (x+34) = 0#
#x = 3 " " or " " x = -34#
The width of the path obviously cannot be negative, so the only answer that we are left with is
We can check this by multiplying
Final Answer