Nala and her cousin agreed that they would each mow one-half of the lawn. The lawn is a 25' by 45' rectangle. The lawn mower cuts a path two feet wide. Nala starts at one corner and mows a path completely around the outside, and then continues to mow the outermost strips working her way inward. If she continues to mow like this, how many times should she go around to mow one half of the lawn?
Total area = 25*45 = 1125 sq.ft.
Half of the area = 562.5 sq.ft
What is needed is the size of the inside rectangle left, or
(25-x)(45-x)=562.5
Solve for x to get x=9.26' and reject the other root which exceeds 25.
Since 9.26'/2'=4.63 strips, so Nala has to go around the lawn between 4 and 5 times to do half the lawn.
Since going around once reduces the width and length by 4',
9.26'/4'=2.315
Nala would need to mow around the lawn between 2 to 3 times to finish half the work.
To calculate how many times Nala should go around to mow one half of the lawn, we need to understand her mowing pattern.
Nala starts at one corner and mows a path completely around the outside of the lawn. The total distance around the outside is the perimeter of the rectangle. Since only one half of the lawn needs to be mowed, we need to find the perimeter of half of the lawn.
The lawn is a 25' by 45' rectangle. To find the perimeter of half of the lawn, we need to calculate the perimeter of the original rectangle and then divide it by 2.
The formula for the perimeter of a rectangle is:
Perimeter = 2 * (Length + Width)
Using this formula, we can calculate the perimeter of the rectangle and then divide it by 2 to get the perimeter of half of the lawn.
Perimeter of the whole lawn:
P = 2 * (25 + 45)
P = 2 * 70
P = 140 feet
Perimeter of half of the lawn = 140 feet / 2 = 70 feet
Now that we know the perimeter of half of the lawn is 70 feet, we can determine how many times Nala needs to go around to mow this distance.
Nala's mowing pattern is to mow a path completely around the outside, and then continues to mow the outermost strips working her way inward. This means that each time she goes around, the perimeter of what she needs to mow decreases by the width of the lawn mower's path, which is 2 feet.
So, to find out how many times Nala needs to go around, we divide the perimeter of half of the lawn by the width of the lawn mower's path.
Number of times Nala needs to go around = Perimeter of half of the lawn / Width of the lawn mower's path
Number of times Nala needs to go around = 70 feet / 2 feet = 35
Therefore, Nala needs to go around 35 times to mow one-half of the lawn.