SOLUTION: Please help! At a point on the ground 24ft from the base of a tree, the distance to the top of the tree is 4ft more than 3 times the height of the tree. Find the height of the tr

Question 1080040: Please help!
At a point on the ground 24ft from the base of a tree, the distance to the top of the tree is 4ft more than 3 times the height of the tree. Find the height of the tree.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
This is a right triangle with one leg 24 ft, the other leg (height) x, and the hypotenuse (3x+4)
24^2+x^2=(3x+4)^2
576+x^2=9x^2+24x+16
0=8x^2+24x-560, divide both sides by 8
0=x^2+3x-70
0=(x+10)(x-7)
x=7 ft, only positive root
The legs are 7, 24 and (3x+4)=25, which is a 7-24-25 right triangle (one of the classics).
The height is 25 feet.

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