SOLUTION: The length of a rectangle is 3 times its width. The diagonal is 2 more than the length. Find the width of the rectangle. please and thank you!((:

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Question 733236: The length of a rectangle is 3 times its width. The diagonal is 2 more than the length. Find the width of the rectangle.
please and thank you!((:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The length of a rectangle is 3 times its width.
The diagonal is 2 more than the length.
Find the width of the rectangle.
:
Let L = the Length
Let W = the width
;
Write an equation for each statement:
:
"The length of a rectangle is 3 times its width."
L = 3W
:
"The diagonal is 2 more than the length."
let c = the diagonal
then
c = (L+2)
or, since L = 3W we can write it
c = (3W+2)
The diagonal is the hypotenuse of the two right triangles
formed by the rectangle:
:
Using Pythag a^2 + b^2 = c^2
then we have:
(3W)^2 + W^2 = (3W+2)^2
FOIL
9W^2 + W^2 = 9W^2 + 6W + 6W + 4
10W^2 = 9W^2 + 12W + 4
Combine like terms on the left
10W^2 - 9W^2 - 12W - 4 = 0
W^2 - 12W - 4 = 0
solve this using the quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
in this problem: x=w; a=1; b=-12; c=-4
w+=+%28-%28-12%29+%2B-+sqrt%28-12%5E2-4%2A1%2A-4+%29%29%2F%282%2A1%29+
w+=+%2812+%2B-+sqrt%28144%2B16+%29%29%2F2+
the reasonable solution
w+=+%2812+%2B+12.65%29%2F2+
w = 24.65%2F2
w = 12.325 is the width
:
:
:
You can check this; find the hypotenuse with legs of 3(12.325)
and 12.325.
It should be 2 units more than the Length which is 3 times the width