A field hockey tournament is to be held in Yellowknife, NWT. According to regulations, the field is 25 yards by 100 yards. For officials, support groups and team members, a uniform rectangular strip of manicured lawn is to be installed by a local business group. If the area of the manicured lawn is twice the surface area of the playing field, how wide will this strip be to the nearest tenth of a meter?
Need help for how to solve this equation.
A = 2 * 25 * 100 = 5000 Sq. Yds. = Area of the lawn,
A = L * W = 5,000,
100W = 5,000,
W = 50 Yds.
well, the dimensions of each end is (25+2w)w and the side (100w). the total lawn area
A=2(25+2w)w+2(100w)=50w+4w^2+200w=4w^2+250w=2*2500
4w^2+250w-5000=0
w^2+62.5w-1250=0
solve the equation.
check my thinking
d
well, (100+2w)(25+2w) = 3 (100*25)
2500 + 250 w + 4 w^2 = 7500
w^2 + 62.5 w - 1250 = 0
agree with bobpursley
To solve this equation, we can follow these steps:
1. Determine the surface area of the playing field:
The playing field is rectangular with dimensions of 25 yards by 100 yards. To find the surface area, we multiply these dimensions: 25 yards * 100 yards = 2500 square yards.
2. Determine the desired surface area of the manicured lawn:
The question states that the area of the manicured lawn should be twice the surface area of the playing field. So, we multiply the surface area of the playing field by 2: 2500 square yards * 2 = 5000 square yards.
3. Convert the surface area of the manicured lawn to meters:
Since the question asks for the width of the strip in meters, we need to convert square yards to square meters. Since 1 yard is approximately 0.9144 meters, we can use this conversion factor.
5000 square yards * (0.9144 meters/1 yard)^2 = 4205.28 square meters.
4. Determine the width of the strip:
The width of the strip is the unknown value in this equation. Let's say it is "w" meters.
The length of the strip will be the same as the length of the playing field, which is 100 yards or 91.44 meters (approximately).
The area of the strip is then given by the equation: length * width = 4205.28 square meters.
Hence, 91.44 meters * w = 4205.28 square meters.
5. Solve for the width of the strip:
To find the width of the strip, we divide both sides of the equation by the length, which is 91.44 meters:
w = 4205.28 square meters / 91.44 meters ≈ 45.98 meters.
Therefore, the width of the strip, rounded to the nearest tenth of a meter, is approximately 46.0 meters.