SOLUTION: A rectangular painting has dimensions X and X+10. the painting is in a frame 2 in. wide. The total area of the picture and the frame is 900 in^2. What are the dimensions of the pai
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Question 143280: A rectangular painting has dimensions X and X+10. the painting is in a frame 2 in. wide. The total area of the picture and the frame is 900 in^2. What are the dimensions of the painting?
Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
(X+2*2)(X+10+2*2)=900
(X+4)(X+10+4)=900
(X+4)(X+14)=900
X^2+18X+56-900=0
X^2+18X-844=0
USING THE QUADRATIC EQUATION WE GET:
X=(-18+-SQRT[18^2-4*1*-844])/2*1
X=(-18+-SQRT[324+3376])/2
X=(-18+-SQRT3700)/2
X=(-18+-60.83)/2
X=(-18+60.38)/2
X=42.82/2
X=21.41 IS THE SHORT SIDE OF THE PICTURE.
21.41+10=31.41 IS THE LONG SIDE OF THE PICTURE.
PROOF:
(21.41+4)(31.41+4)=900
25.41*35.41=900
899.77~900
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