Suppose each diagonal of a rectangle is of length 17 while the area is 120. Find the perimeter of the rectangle.
+36916 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
+36916 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
