Jackie mows a strip of uniform width around her 25 m by 15 m rectangular lawn and leaves a patch of lawn that is 60 percent of the original equation. what is the width of the strip
Well, Jackie seems to have done a lot of mower-ing! To find the width of the strip, we need to determine the area of the patch left by Jackie, and then divide it by the original width of the lawn.
First, let's calculate the area of the original lawn:
Original Area = Length * Width
Original Area = 25 m * 15 m
Original Area = 375 square meters
Now, let's find the area of the patch left by Jackie:
Patch Area = 60% of Original Area
Patch Area = (60/100) * 375 square meters
Patch Area = 225 square meters
Since Jackie mowed a strip around the lawn, the area of the strip can be found by subtracting the patch area from the original area:
Strip Area = Original Area - Patch Area
Strip Area = 375 square meters - 225 square meters
Strip Area = 150 square meters
Now, we need to find the width of the strip. We know that the strip has a uniform width, so all four sides of the strip have the same length. Let's assume the width of the strip is "w" meters.
Using the formula for the area of a rectangle, we can write the equation:
Strip Area = Length of Strip * Width of Strip
150 square meters = (25 + 2w) * (15 + 2w)
Unfortunately, this equation is starting to look like a lawn-mowing maze! It's not easy to solve analytically. We need some trickier tools for this one. Let's call in the experts!
To find the width of the strip mowed around Jackie's lawn, we need to calculate the area of the original lawn.
The area of a rectangle is given by the formula: length x width.
Given that the length of the lawn is 25 meters and the width is 15 meters, the area of the original lawn is:
25 m x 15 m = 375 square meters.
Jackie mowed a strip around her lawn, leaving a patch that is 60% of the original area. To find the area of the patch, we can multiply the original area by 0.60:
375 square meters x 0.60 = 225 square meters.
The patch left after mowing is 225 square meters.
Let's assume the width of the strip mowed around the lawn is 'x' meters.
When we add the width of the strip to both the length and the width of the original lawn, the length becomes (25 + 2x) and the width becomes (15 + 2x). The area of the larger rectangle (with the strip mowed) is then given by:
Area = Length x Width
Area = (25 + 2x) * (15 + 2x)
Since the patch left is 60% of the original area, the equation becomes:
225 = 0.60 * (25 + 2x) * (15 + 2x)
225 = 0.6 * (375 + 90x + 50x + 4x^2)
225 = 0.6 * (375 + 140x + 4x^2)
225 = 225 + 84x + 2.4x^2
0 = 84x + 2.4x^2
Dividing by 2.4 to simplify the equation:
0 = 35x + x^2
Now, to find the width of the strip (x), we need to solve this equation. We can do this by factoring or by using the quadratic formula. Since it's a quadratic equation, we'll use the quadratic formula.
The quadratic formula states that for an equation in the form of ax^2 + bx + c = 0, the solution can be found using:
x = (-b ± √(b^2 - 4ac))/(2a)
In our equation, a = 1, b = 35, and c = 0.
Plugging the values into the formula:
x = (-35 ± √(35^2 - 4*1*0))/(2*1)
x = (-35 ± √(1225))/(2)
x = (-35 ± 35)/(2)
This results in two possible values for x:
x1 = (-35 + 35)/2 = 0/2 = 0
x2 = (-35 - 35)/2 = -70/2 = -35
Since the width cannot be negative, the width of the strip mowed around Jackie's lawn is 0 meters.
To find the width of the strip, we need to determine the length and width of the remaining patch of lawn.
Let's assume the width of the strip is "x". Therefore, the new length of the rectangle after mowing will be (25 - 2x) meters, and the new width will be (15 - 2x) meters.
According to the question, the patch of lawn that remains is 60% of the original area. This means that the remaining area is 0.60 times the area of the original lawn.
Original Area = Length * Width
Remaining Area = (25 - 2x) * (15 - 2x)
Now we can set up an equation using the given information:
Remaining Area = 0.60 * Original Area
(25 - 2x) * (15 - 2x) = 0.60 * 25 * 15
Simplify the equation:
(375 - 50x - 30x + 4x^2) = 0.60 * 375
375 - 80x + 4x^2 = 0.60 * 375
4x^2 - 80x + 375 - 0.60 * 375 = 0
Combine like terms:
4x^2 - 80x + 375 - 225 = 0
4x^2 - 80x + 150 = 0
Now we can solve this quadratic equation for x. Use factoring or the quadratic formula to find the solutions for x.
After finding the values of x, you will have the possible widths for the strip around the lawn.
25x15=375 of 60%
=375x60/100
=225
I am not 100% sure that its correct. Still Iwould say 50 /50