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Suppose each diagonal of a rectangle is of length 17 while the area is 120. Find the perimeter of the rectangle.

 Jan 7, 2020

Best Answer 

 #1
avatar+19815 
+2

l * w = 120     w = 120/l

 

l^2 + w^2 = 17^2 = 289

 

Substitute in the value of w

 

l^2 + 120^2/l^2 = 289     Multiply both sides by l^2

 

l^4 + -289 l^2 + 14400  = 0        let x = l^2

x^2 - 289x + 14400 =0       Quadratic formula reveals  x = 225  or 64

 

then l^2 = 225   or 64

        l = 15   or 8

         then w = 8 or 15       l x w  = 8x15=120    or   l x w = 15 x 8 = 120   

perimeter = 2l+ 2w = 2(15) + 2(8) = 46

 Jan 7, 2020
 #1
avatar+19815 
+2
Best Answer

l * w = 120     w = 120/l

 

l^2 + w^2 = 17^2 = 289

 

Substitute in the value of w

 

l^2 + 120^2/l^2 = 289     Multiply both sides by l^2

 

l^4 + -289 l^2 + 14400  = 0        let x = l^2

x^2 - 289x + 14400 =0       Quadratic formula reveals  x = 225  or 64

 

then l^2 = 225   or 64

        l = 15   or 8

         then w = 8 or 15       l x w  = 8x15=120    or   l x w = 15 x 8 = 120   

perimeter = 2l+ 2w = 2(15) + 2(8) = 46

ElectricPavlov Jan 7, 2020

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