A rectangular park measuring 35 yards by 24 yards is surrounded by a trail of uniform width. If the area of the park and the trail combined is 2420 square yards, what is the width of the path?
outside dimension
length = 35+2x
width = 24+2x
solve
(35+2x)(24+2x) = 2420
You will have to know how to solve a quadratic equation
To find the width of the path, we first need to determine the total area of the park and the trail combined.
The area of a rectangle is given by its length multiplied by its width. In this case, the park measures 35 yards by 24 yards, so its area is 35 * 24 = 840 square yards.
Let's represent the width of the path as 'x' yards. The overall dimensions of the park and the trail will be increased by twice this width, as there is a path on both sides of the park. So, the length of the entire rectangular area (park + trail) is 35 + 2x yards, and the width is 24 + 2x yards.
The area of the overall rectangular area (park + trail) can be calculated by multiplying its length and width. In this case, the total area is given as 2420 square yards. So, we have the equation:
(35 + 2x) * (24 + 2x) = 2420
Expanding this equation gives us:
840 + 70x + 48x + 4x^2 = 2420
Combining like terms:
4x^2 + 118x + 840 = 2420
Rearranging the equation:
4x^2 + 118x + 840 - 2420 = 0
4x^2 + 118x - 1580 = 0
Now we can solve this quadratic equation to find the possible values of 'x', which represents the width of the path.