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ps 31

by dunkin77 » Tue Jun 19, 2007 5:20 pm
A small, rectangular park has a perimeter of 560 feet and a diagonal measurement of 200 feet. What is its area, in square feet?

A. 19,200
B. 19,600
C. 20,000
D. 20,400
E. 20,800


2x+2y = 560

x^2 + y^2 =200
x+y=10sqrt2

so,
2x+2(10sqrt2 -x)=560
then
x becomes 0...

Can anyone explain where did I do wrong? :oops:
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Re: ps 31

by Neo2000 » Tue Jun 19, 2007 6:06 pm
dunkin77 wrote:
2x+2y = 560

x^2 + y^2 =200
x+y=10sqrt2

so,
2x+2(10sqrt2 -x)=560
then
x becomes 0...

Can anyone explain where did I do wrong? :oops:
This should read as
x^2 + y^2 =40000
since the diagonal is Root of Sum of Squares of the two sides.(Pythagoras Theorem)
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by dunkin77 » Tue Jun 19, 2007 6:28 pm
Oops, thank you.

but still if I substitute..

2x+2(200-x) = 560

x get zero...
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Re: ps 31

by Neo2000 » Tue Jun 19, 2007 6:49 pm
dunkin77 wrote:A small, rectangular park has a perimeter of 560 feet and a diagonal measurement of 200 feet. What is its area, in square feet?

A. 19,200
B. 19,600
C. 20,000
D. 20,400
E. 20,800


2x+2y = 560

x^2 + y^2 =200
x+y=10sqrt2
x+y = 280
x^2 + y^2 =40000
(X+y)^2 = x^2 +y^2 +2xy

(280)^2 -(200)^2 = 2xy
480 x80 = 2xy
xy = 240x80 = 19200
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