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

Question 322752: Ethan cuts half a rectangular lawn 40 m by 30 m by mowing a strip of equal width around the perimeter. Julia cuts the small rectangle left. How wide a strip does Ethan cut so that they share the work equally?
Found 2 solutions by solver91311, ankor@dixie-net.com:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Since Ethan cuts a strip meters wide all the way around, each of the dimensions of the rectangle left for Julia is the original dimension reduced by . The entire lawn area is 30 times 40 meters or 1200 square meters. That means we need to choose so that Julia's piece which measures by is half of that area or 600 square meters.

Expand the binomials, put the equation in standard form, and then solve the resulting quadratic for .

John

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Ethan cuts half a rectangular lawn 40 m by 30 m by mowing a strip of equal width around the perimeter.
Julia cuts the small rectangle left.
How wide a strip does Ethan cut so that they share the work equally?
:
Let x = the width of the strip cut by E
:
Find the total area of the lawn; 40 * 30 = 1200 sq/m
Each will mow an area of 600 sq/m
:
Dimension of the small rectangle which is 600 sq/ft:
(40-2x) by (30-2x)
;
Write an area equation of this rectangle. find x, which is the width of the strip
(40-2x)(30-2x) = 600
FOIL
1200 - 80x - 60x + 4x^2 = 600
Arrange as a quadratic equation
4x^2 - 140x + 1200 - 600 = 0
4x^2 - 140x + 600 = 0
Simplify divide by 4
x^2 - 35x + 150 0 =
Factor
(x - 5)(x - 30) = 0
The reasonable solution
x = 5 ft is the width of the strip
:
:
Check solution by finding the area of the inside rectangle
(40-10)*(30-10) = 600

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