SOLUTION: Please help me solve this. Diane's Frame Shop is building a frame for a rectangular painting with an area of 120 in^2 and a diagonal of 17 in. Find the dimensions of the paintin

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Question 247436: Please help me solve this.
Diane's Frame Shop is building a frame for a rectangular painting with an area of 120 in^2 and a diagonal of 17 in. Find the dimensions of the painting.

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
a frame for a rectangular painting with an area of 120 in^2 and a diagonal of 17 in.
:
Area:
L * W = 120
L = 120%2FW
:
Find the dimensions of the painting.
L by W
Using pythag a^2 + b^2 = c^2
we have:
L^2 + W^2 = 17^2
L^2 + W^2 = 289
:
Substitute for L
(120%2FW)^2 + W^2 = 289
14400%2FW%5E2 + W^2 = 289
:
Mult by W^2, results
14400 + W^4 = 289W^2
:
Arrange as a quadratic equation
W^4 - 298W^2 + 14400 = 0
:
This will factor to
(W^2 - 225)(W^2 - 64)
:
Two solutions
W^2 = 225
W = 15
and
W^2 = 64
W = 8; this is the one we will call the Width
Find L
L = 120/8
L = 15
:
The dimensions of the painting: 15 by 8
:
Check by finding the diagonal
15^2 + 8^2 = 17^2
225 + 64 = 289