SOLUTION: A rectangular garden measures 40 m times 20 m. It is surrounded by a walkway of uniform width so that the combined area of the garden and walkway is twice the area of just the gard

Algebra ->  Exponents -> SOLUTION: A rectangular garden measures 40 m times 20 m. It is surrounded by a walkway of uniform width so that the combined area of the garden and walkway is twice the area of just the gard      Log On


   

Question 888369: A rectangular garden measures 40 m times 20 m. It is surrounded by a walkway of uniform width so that the combined area of the garden and walkway is twice the area of just the garden. Determine the width of the walkway to the nearest 10th of a meter
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
Garden area is 40*20 square meters.

Let w = width of the walkway.

Combined area of the garden and walkway is (2w+40)(2w+20) square meters.

Twice the area of just the garden is 2*40*20.

Take the description from the second sentence and put into a meaningful equation:
" combined area of the garden and walkway is twice the area of just the garden"

highlight_green%28%282w%2B40%29%282w%2B20%29=2%2A40%2A20%29
Solve this for w.
The obvious factored form as first shown here allows simplification by common factor elimination before going into multiplications.
-
2%2A2%28w%2B20%29%28w%2B10%29=2%2A2%2A2%2A10%2A20
%28w%2B20%29%28w%2B10%29=20%2A20
w%5E2%2B30w%2B200=400
w%5E2%2B30w=200
highlight_green%28w%5E2%2B30w-200=0%29
? Factorable?
Discriminant, 900+4*200=900+800=1700=100*17, therefore not factorable.
w=%28-30%2Bsqrt%28100%2A17%29%29%2F2
w=%28-30%2B10sqrt%2817%29%29%2F2
highlight%28w=5sqrt%2817%29-15%29
-
5.6 meters