Thread: polynomial equation- Algebra 2 help

a rectangular garden is 10ft wide and 12ft long. a walk of uniform width surrounds the garden. if the total area of the garden and the walk is 168ft squared , what is the width of the walk?

can you help... I don't understand the problem, I can do the work but I end up with negatve answers.

Originally Posted by pieman396

a rectangular garden is 10ft wide and 12ft long. a walk of uniform width surrounds the garden. if the total area of the garden and the walk is 168ft squared , what is the width of the walk?

can you help... I don't understand the problem, I can do the work but I end up with negatve answers.

Let's see here


let the width of the walk be x. since the walk surrounds the garden, the width of the garden is going to be it's width + 2x and the length of the garden is going to be it's length + 2x.

now just plug these values into the area equation:

we have length = 12 + 2x
we have width = 10 + 2x
area = length*width

=> area = 168 = (12 + 2x)(10 + 2x)

=> (12 + 2x)(10 + 2x) = 168
=> 120 + 44x + 4x^2 = 168 ............i expanded the brackets
=> 30 + 11x + x^2 = 42 .................i divided through by 4
=> x^2 + 11x - 12 = 0
=> (x + 12)(x - 1) = 0
=> x + 12 = 0, or x - 1 = 0
=> x = -12 or x = 1

x cannot be minus 12, since it's a length
so x = 1 ft

so the width of the walk is 1 ft