If the length of football field is 40 yards ; than three times the width. the total area 6400 sq, yards what are the dimensions.
L = 3W - 40
L * W = 6400
(3W-40) * W = 6400
Solve for W, then L.
To find the dimensions of the football field, we can set up a system of equations using the given information.
Let's assume the width of the field is w yards.
According to the given information, the length of the field is 40 yards less than three times the width. So, the length would be (3w - 40) yards.
The total area of a rectangle can be calculated by multiplying its length by its width. In this case, the area is given as 6400 sq. yards.
So, we have the equation:
Area = Length × Width
6400 = (3w - 40) × w
To solve this equation for w, we can expand and rearrange:
6400 = 3w^2 - 40w
Combining like terms, we get:
3w^2 - 40w - 6400 = 0
Now, we can solve this quadratic equation using either factoring, completing the square, or the quadratic formula.
Using the quadratic formula, which is a general method to solve quadratic equations:
w = (-b ± sqrt(b^2 - 4ac)) / 2a
In this case, a = 3, b = -40, and c = -6400.
Plugging in these values into the quadratic formula:
w = (-(-40) ± sqrt((-40)^2 - 4(3)(-6400))) / 2(3)
Simplifying further:
w = (40 ± sqrt(1600 + 76800)) / 6
w = (40 ± sqrt(78400)) / 6
w = (40 ± 280) / 6
Now, we have two possible values for the width, so let's calculate both:
w1 = (40 + 280) / 6 = 320 / 6 = 53.33 yards (rounded to two decimal places)
w2 = (40 - 280) / 6 = -240 / 6 = -40 yards (negative value, which doesn't make sense in this context)
Since the width cannot be negative, we discard the second value.
Therefore, the width of the football field is approximately 53.33 yards.
To find the length, we can substitute this value of w into the length equation: (3w - 40)
Length = 3w - 40
Length = 3(53.33) - 40
Length = 159.99 - 40
Length ≈ 119.99 yards (rounded to two decimal places)
Therefore, the dimensions of the football field are approximately:
Width: 53.33 yards
Length: 119.99 yards