A rectangle contains a strip of width $1,$ as shown below. Find the area of the strip.
Let x be the length from the right edge to the strip.
We have
[rectangle]=1⋅√82+x2+8x=10⋅8√82+x2=80−8x82+x2=6400−1280x+64x263x2−1280x+6336=0
x=−b±√b2−4ac2a=640−8√16363x=8.5375[strip]=1⋅√8.53752+82[strip]=11.7
Thanks! :)