SOLUTION: The hypotenuse of a right triangle is 1 foot longer than one of the sides. If the other side was 1 foot longer, it would be exactly one third the length of the first side. Find the

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Question 1053258: The hypotenuse of a right triangle is 1 foot longer than one of the sides. If the other side was 1 foot longer, it would be exactly one third the length of the first side. Find the length of each of the sides, and of the hypotenuse.
Found 2 solutions by Boreal, josmiceli:
Answer by Boreal(15235) (Show Source):
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hypotenuse=x
one side is x-1
the third side is x^2-(x-1)^2, which is sqrt {x^2-(x^2-2x+1)}=sqrt (2x-1).
adding 1 to the third side makes it sqrt(2x-1)+1=(1/3)(x-1)=(1/3)x-(1/3)
sqrt(2x-1)=(1/3)x-(4/3)
square both sides
2x-1=(1/9)x^2-(8/9)x+(16/9)
0=(1/9)x^2-(26/9)x+(25/9)
multiply everything by 9
0=x^2-26x+25
(x-25)(x-1)=0;
x=25, 1, and 1 is impossible
x-1=24
The third side is 7 (7,24,25 triangle) and 7+1 is 1/3 of 24.

Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website!
let the sides and the hypotenuse of the triangle be:
, , and ( in feet )
--------------------------
given:
(1)
(2)
(3) ( pythagorean theorem )
--------------------------
(2)
Substitute (1) and (2) into (3)
(3)
(3)
(3)
(3)
(3)

and
(1)
(1)
(1)
and
(2)
(2)
(2)
The sides are 7, 24, and 25
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check answer:
(3)
(3)
(3)
(3)
You can check (1) and (2)