# 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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 Click here to see ALL problems on Miscellaneous Word Problems 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(15746)   (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 = : 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 ()^2 + W^2 = 289 + 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