If the perimeter of a rectangle is 20 feet and the diagonal is 2 (sqrt{13}) feet, then what are the length and width?

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- Nov 1st 2008, 10:39 PMmagentaritaFind Length and Width of Rectangle
If the perimeter of a rectangle is 20 feet and the diagonal is 2 (sqrt{13}) feet, then what are the length and width?

- Nov 1st 2008, 11:35 PMips_math
if length = x ft and breadth = y ft

then by given condition 2(x+y) = 20 .....(1)

and x^2 + y^2 = (2sqr(13))^2 = 52 .....(2)

from eq(1) x+y = 10........(3)

from eq (2) & eq(3)

2xy=(x+y)^2 -(x62+y^2) = 100-52 = 48

now (x-y)^2 = x^2+y^2 - 2xy =52 - 48 =4

or x-y =2 .......(4)

solving (3) & (4) we get

length (x) =6 ft

breadth (y) = 4 ft - Nov 3rd 2008, 05:59 AMmagentaritamuch better.....