A field hockey tournament is to be held in Yellowknife, NWT. According to regulations, the field is 25 yds by 100yds. For officials, support group 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 metre?
let the width of the lawn be x yds
field --- 25 yds by 100 yds
area = 2500 yds^2
field including the lawn around it:
(25+2x) by (100+2x) yds
area = (25+2x)(100+2x) yds^2
area of lawn = (25+2x)(100+2x) - 2500
you said:
(25+2x)(100+2x) - 2500 = 2(2500)
2500 + 250x + 4x^2 - 2500 - 5000 = 0
4x^2 + 250x - 5000 = 0
2x^2 + 125x - 2500 = 0
use the formula to find the positive value of x
btw, Yellowstone would not use yards to measure, it would use metres, the units you requested in your answer. I was teaching back in the days when we switched form the old system to metric and many text books simply switched the name of the units, often resulting in ridiculous answers. Hope you are not using a text from that era.
reiny is coorect
To find the width of the strip, we first need to calculate the surface area of the playing field and then divide it by 2 to find the area of the manicured lawn.
The surface area of a rectangular shape is found by multiplying its length by its width. In this case, the length of the playing field is 100 yards and the width is 25 yards, so the surface area of the playing field is:
100 yards (length) * 25 yards (width) = 2500 square yards.
Since the area of the manicured lawn is twice the surface area of the playing field, we need to calculate:
2 * 2500 square yards = 5000 square yards.
To convert the area from square yards to square meters, we need to multiply by a conversion factor. One square yard is approximately equal to 0.836 square meters, so:
5000 square yards * 0.836 square meters/square yard = 4180 square meters.
Now, to calculate the width of the strip, we need to rearrange the formula for surface area to solve for width:
Surface area = length * width
In this case, we know the length of the strip is 100 yards. Let's call the width of the strip "w" for now. So, the equation becomes:
4180 square meters = 100 yards * w
To solve for "w," we need to convert the length from yards to meters. One yard is equal to approximately 0.9144 meters, so:
100 yards * 0.9144 meters/yard = 91.44 meters.
Now, let's solve for "w":
4180 square meters = 91.44 meters * w
Dividing both sides by 91.44 meters:
4180 square meters / 91.44 meters = w
The width of the strip, to the nearest tenth of a meter, is approximately 45.7 meters.