A rectangular plot of ground having dimensions 24 feet by 26 feet is surrounded by a walk of uniform width. If the area of the walk is 104 feet squared, what is its width?
True, but that gets 0 points.
If the walk is w feet wide, then the inside dimensions are 24x26 and the outer dimensions are 24+w and 26+w. So, the area of the walk is the outer area minus the inner area.
(26+2w)(24+2w) - 26*24 = 624 + 100w + 4w^2 - 624 = 104
4w^2 + 100w - 104 = 0
w^2 + 25w + -26 = 0
(w-1)(w+26) = 0
So, w = 1 (-26 makes no physical sense)
26*28 - 26*24 = 26*4 = 104 as wanted.
To find the width of the walk, we need to subtract the area of the rectangular plot from the total area, which includes the plot and the walk.
We are given that the dimensions of the rectangular plot are 24 feet by 26 feet. This gives us the area of the plot: 24 feet * 26 feet = 624 square feet.
The total area, including the plot and the walk, is given to be 104 square feet more than the area of the plot, so it can be represented as: 624 square feet + 104 square feet = 728 square feet.
Let's assume the width of the walk is x. The length of the rectangle, including the walk, would be (24 + 2x), and the width, including the walk, would be (26 + 2x).
The area of the total region can be calculated as the product of the length and the width, which gives us the following equation: (24 + 2x) * (26 + 2x) = 728.
To solve this equation, we can multiply it out: 624 + 68x + 52x + 4x^2 = 728.
Combine like terms: 4x^2 + 120x + 624 = 728.
Rearrange the equation to bring all terms to one side: 4x^2 + 120x + 624 - 728 = 0.
Simplify the equation: 4x^2 + 120x - 104 = 0.
Now we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula.
If we solve this equation, we find that the width of the walk is approximately 2 feet.