SOLUTION: The hypotenuse of a right triangle is 16 in. longer than the shortest side and 2 in. longer than the remaining side. Find the dimensions of this triangle. What is the length of

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Question 548549: The hypotenuse of a right triangle is 16 in. longer
than the shortest side and 2 in. longer than the remaining side. Find the dimensions of this triangle. What is the length of the shortest side (in inches)?

Found 2 solutions by mananth, stanbon:
Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website!
let the hypotenuse be x
it is 16 in longer than the shortest side
so shortest side = x-16
other side = x-2
By Pythagoras theorem
(x-2)^2+(x-16)^2=x^2
x^2-4x+4+x^2-32x+256=x^2
x^2-36x+260=0
x^2-26x-10x+260=0
x(x-26)-10(x-26)=0
(x-26)(x-10)=0
x=26 OR 10
Only 26 is possible
shortest side = 26-16=10
other side = 24
The sides are 10,24,26
CHECK
10^2+24^2=676 = 26^2

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
The hypotenuse of a right triangle is 16 in. longer than the shortest side and 2 in. longer than the remaining side. Find the dimensions of this triangle. What is the length of the shortest side (in inches)?
---------
Let shortest side be "x":
Then hypotenuse is "x+16":
3rd side is "x+14":
-------------------------
Equation:
x^2 + (x+14)^2 = (x+16)^2
-----
x^2 + x^2+28x+14^2 = x^2 + 32x + 16^2
----
x^2 - 4x - 60 = 0
----
x^2-10x+6x-60 = 0
x(x-10)+6(x-10) = 0
(x-10)(x+6) = 0
Positive solution:
x = 10 (shortest)
x+16 = 26 (hypotenuse)
x+14 = 24 (3rd side)
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Cheers,
Stan H.
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