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) (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
in this problem: x=w; a=1; b=-12; c=-4
the reasonable solution
w =
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
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