SOLUTION: Word problem help. There is a closet door whose height is 4ft more than its width. To keep the closet closed a cable is attached diagonally from one corner to the other. If the cab

Question 151487: Word problem help. There is a closet door whose height is 4ft more than its width. To keep the closet closed a cable is attached diagonally from one corner to the other. If the cable measures sqrt194/2 ft, what are the dimensions of the door?
I thought the height would be: h=4+w and width would be w. But from there I am lost. How would I set this equation up?
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
good so far...

the height and width are two legs of a right triangle with the diagonal cable as the hypotenuse

by Pythagoras __ h^2+w^2=(sqrt(194)/2)^2 __ substituting __ (w+4)^2+w^2=194/4 __ 2w^2+8w+16=194/4

multiplying by 4 __ 8w^2+32w+64=194 __ subtracting 194 __ 8w^2+32w-130=0 __ dividing by 2 __ 4w^2+16w-65=0

factoring __ (2w+13)(2w-5)=0

2w+13=0 __ w=-13/2 __ negative value not realistic

2w-5=0 __ w=5/2 __ substituting h=(5/2)+4 __ h=6.5
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