SOLUTION: The ratio of the length of a rectangle to its width is the same as that of the diagonal to the length. If the width is 2 , how many units are in the length of the diagonal?

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Question 207692: The ratio of the length of a rectangle to its width is the same as that of the diagonal to the length. If the width is 2 , how many units are in the length of the diagonal?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The ratio of the length of a rectangle to its width is the same as that of the diagonal to the length.
If the width is 2 , how many units are in the length of the diagonal?
:
the hypotenuse (diagonal) = h,
h = sqrt%28L%5E2+%2B+w%5E2%29
w=2
h = sqrt%28L%5E2+%2B+2%5E2%29
h = sqrt%28L%5E2+%2B+4%29
:
"the ratio of the length of a rectangle to its width is the same as that of the diagonal to the length.
L%2FW = h%2FL
:
Replace W with 2; and h with sqrt%28L%5E2+%2B+4%29
L%2F2 = %28sqrt%28L%5E2+%2B+4%29%29%2FL
Cross multiply
L*L = 2sqrt%28L%5E2+%2B+4%29
:
L^2 = 2sqrt%28L%5E2+%2B+4%29
:
Square both sides:
L^4 = 4(L^2 + 4)
:
L^4 = 4L^2 + 16
:
L^4 - 4L^2 - 16 = 0
:
You have to use the quadratic formula to find L^2
a-1; b=-4; c=-16
The positive solution was L^2 = 6.472
:
Use the value to find the diagonal
h = sqrt%286.472+%2B+2%5E2%29
h = sqrt%2810.472%29
h = 3.236 units is the diagonal
:
:
Check solution
L = sqrt%286.472%29 = 2.544
L%2FW = h%2FL
2.554%2F2 = 3.236%2F2.554
1.272 = 1.272