Lisa, Nicole, and Amber are to mow a rectangular lawn that measures 100 feet by 120 feet. Lisa is going to mow one0third of the lawn by mowing a strip of niform width around the outer edge of the lawn. What are the dimensions of the lawn to still be mowed?
total area = 12000 ft^2
still to be mowed = (1/2)(12000) = 8000 ft^2
let the width mowed by Lisa be x ft wide
area still to be done
= (100-2x)(120-2x)
= 12000-200x - 240x + 4x^2
4x^2 - 440x + 12000 = 8000
x^2 - 110x + 1000 = 0
(x-100)(x -10) = 0
x = 100 or x = 10 , but clearly
100-2x > 0
-2x > -100
x < 50
so x = 10 and the lawn left to be cut is
80 by 100 ft
To find the dimensions of the lawn to still be mowed, we need to subtract the area Lisa is going to mow from the total area of the lawn.
First, let's find the area of the lawn. The area of a rectangle can be calculated by multiplying its length by its width. In this case, the length is 100 feet and the width is 120 feet. So, the total area of the lawn is 100 feet * 120 feet = 12,000 square feet.
Next, let's find the area that Lisa is going to mow. Lisa is going to mow one-third of the lawn by mowing a strip of uniform width around the outer edge of the lawn.
To find the width of the strip that Lisa is going to mow, we need to divide the length of the lawn (100 feet) by 3, because Lisa is mowing one-third of the lawn. So, the width of the strip is 100 feet / 3 = 33.33 feet (rounded to two decimal places).
To find the length and width of the lawn to be mowed, we need to subtract the width of the strip from the original dimensions of the lawn.
The new length of the lawn would be 100 feet - (2 * width of the strip) because there are two lengths and two widths. So, the new length would be 100 feet - (2 * 33.33 feet) = 33.34 feet.
Similarly, the new width of the lawn would be 120 feet - (2 * width of the strip) = 120 feet - (2 * 33.33 feet) = 53.34 feet.
Therefore, the dimensions of the lawn to still be mowed are 33.34 feet by 53.34 feet.