• Apr 27th 2006, 04:02 PM
sugar_babee
Heres the question:

Two boys agree to mow a rectangular lawn 80m by 60m, each mowing half. The first boy mows a strip of uniform width around the outside of the lawn. how wide is the strip?

So far ive figured out that each boy mows half the area which is 2400m^2, and ive wrote out an equation of the area which is length=2400/width. Now im completely stuck, can someone please help me?
• Apr 27th 2006, 04:26 PM
ThePerfectHacker
Quote:

Originally Posted by sugar_babee
Heres the question:

Two boys agree to mow a rectangular lawn 80m by 60m, each mowing half. The first boy mows a strip of uniform width around the outside of the lawn. how wide is the strip?

So far ive figured out that each boy mows half the area which is 2400m^2, and ive wrote out an equation of the area which is length=2400/width. Now im completely stuck, can someone please help me?

This is what you have,
Rectange 60x80 if the width of the strip around is $x$ then the area needs to be 2400 (half). The area of the smaller rectangle inside is
$(60-2x)(80-2x)=2400$
Then, divide by 4
$(30-x)(40-x)=600$
Thus,
$x^2-70x+1200=600$
Thus,
$x^2-70x+600=0$
Thus,
$(x-10)(x-60)=0$
Thus,
$x=10,60$
It cannot be 60 because that is too much. Thus the width of strip of 10 meters.
• Apr 27th 2006, 04:29 PM
sugar_babee
Thank you so much, i get what i was missing before :)
• Apr 27th 2006, 04:30 PM
topsquark
Quote:

Originally Posted by sugar_babee
Heres the question:

Two boys agree to mow a rectangular lawn 80m by 60m, each mowing half. The first boy mows a strip of uniform width around the outside of the lawn. how wide is the strip?

So far ive figured out that each boy mows half the area which is 2400m^2, and ive wrote out an equation of the area which is length=2400/width. Now im completely stuck, can someone please help me?

Ugh. I really need to get some sort of picture drawing software!

Imagine your rectangle. I'm taking the 80 m to be the horizontal side, which I am going to call the width. One boy is mowing a strip of uniform width around the yard. So say that he mows a strip of width x. The dimensions of the rectangle of lawn left over in the center are going to be: width = 80-2x and length = 60-2x. (There's a strip of size x on EACH side of the lawn, hence the 2x instead of x.)

We know that the interior has an area of 2400 m^2. So
$(80-2x)(60-2x)=2400$

Solve this equation for x and you are done.
$(80-2x)(60-2x)=4x^2-280x+4800=2400$
$4x^2-280x+2400=0$
and thus x = 10 m or x = 60 m using your favorite method of solution.

I hope it's obvious that the 60 m measurement is unphysical. Thus the solution is x = 10 m.

-Dan
• Apr 27th 2006, 04:30 PM
topsquark
Is there an echo in here? :)

-Dan
• Apr 27th 2006, 05:56 PM
MathGuru
is there an echo in here? :)