Question

Alfonse cuts half a rectangular lawn, 50m by 20m, by mowing strips of equal width around the perimeter. Bart cuts the small rectangle in the middle that's left. How wide a strip does Alfonse cut so that they share the work equally?

Answer 1

50 * 20 = 1000

strip width = s

interior dimensions

(50-2s)(20-2s) = half original = 500

1000 - 140 s + 4 s^2 = 500
so
4 s^2 - 140 s +500 = 0

s^2 - 35 s + 125 = 0

s = [35 +/- sqrt (1225-500) ]/2
s = [35+/- 26.92 ] /2
s = 30.96 or 4.04
must be 4.04 because strips of 31 each end will not work
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check
50 - 2(4.04) =41.92
20 - 2(4.04) = 11.92
11.92 * 41.92 = 499.6 fine

Answer 2

gustave is a really demanding student who finishes his work in half the time of other students if he isnt kept busy he takes off his shoes and dances on the desks. His teach assigns him to add the first 5000 odd numbers. come up with the answer and illustrate how gustave can do this fast and get back to his dancing.