SOLUTION: Glenn cuts half a rectangular lawn, 40 m by 30 m, by mowing strips of equal width around the perimeter. Brad cuts the small rectangle left. How wide a strip does Glenn cut so that

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Glenn cuts half a rectangular lawn, 40 m by 30 m, by mowing strips of equal width around the perimeter. Brad cuts the small rectangle left. How wide a strip does Glenn cut so that       Log On


   

Question 825286: Glenn cuts half a rectangular lawn, 40 m by 30 m, by mowing strips of equal width around the perimeter. Brad cuts the small rectangle left. How wide a strip does Glenn cut so that they share the work equally?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
w = the width along perimeter which Glenn cuts.
The whole lawn area is 40*30 m^2.

The area cut, 4w%5E2%2B2%2840-2w%29%2B2%2830-2w%29.

That area cut is half the lawn area.
Solve this equation: 4w%5E2%2B2%2840-2w%29%2B2%2830-2w%29=40%2A30%2F2

Continuing a bit:
2w%5E2%2B%2840-2w%2B30-2w%29=20%2A30%2F2
2w%5E2%2B70-4w=60
2w%5E2-4w%2B60=0
w%5E2-2w%2B30=0 seems not factorable;
w=%282%2Bsqrt%284%2B4%2A30%29%29%2F%282%29
w=%282%2Bsqrt%28124%29%29%2F2
w=%282%2B2%2Asqrt%2830%29%29%2F2
highlight%28w=1%2Bsqrt%2830%29%29