Rectangular garden. Dimensions: 30ft by 40ft. Total area garden plus walkway is to be 1800ft sq.?

Question

Whats the width of walkway to enarest thousandth?

A) 5.430 ft B) 3.860 ft C) 2.610 ft D) 7.720 ft

Answer 1

The correct answer is B.

First let me prove it by simply multiplying it out:

2(30)(3.860) + 2(40)(3.860) + 4(3.860)² = ?
140(3.860) + 4(14.900) = ?
540.400 + 59.600 = 600.000

I will describe the method for determining the answer, but let you work out the details.

First, since we know the area of the garden itself is 1200 ft², then the area of the walk must be 600 ft².

The area of the walk itself can be written as a function of the width and length of the garden plus the width of the walk.

Area(walk) = 2xw' + 2yw' + 4(w')², where x is the width of the garden, y is the length of the garden, and w' is the width of the walk. We know the actual numerical values of x and y, so all we have to do is plug those directly into the above equation. That results in this final equation:

600 = 2(30)w' + 2(40)w' + 4(w')²
600 = 60w' + 80w' + 4(w')²
600 = 140w' + 4(w')²
0 = 4(w')² + 140w' - 600

Now you have a quadratic equation in terms of the width of the walk which can be easily solved using the quadratic formula. Divide through by 4 first to simplify calculations.