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?

Question

Reiny · Answer

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.

bage · Answer

reiny is coorect