SOLUTION: Hypotoneuse Headaches! Please help me! I cannot figure these out. Been wrong 4 times... 1. The hypotenuse of a right triangle is 16 in. longer than the shortest side and 2 in.

Question 490728: Hypotoneuse Headaches! Please help me! I cannot figure these out. Been wrong 4 times...
1. 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 remaining side (in inches)?
2. 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 hypotenuse (in inches)?
3. 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 Alan3354, scott8148:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
1. 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 remaining side (in inches)?
--------------
c = hypotenuse
a = short side, b = longer side
--------------
c = a+16 --> a = c-16
c = b+2 --> b = c-2
---------

(c - 10)*(c - 26) = 0
c = 10, c = 26
---------------
c = 10 doesn't work since a = -6
---------------
c = 26
b = 10
a = 24
---------
It's the 5, 12, 13 right triangle x2

Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
the three sides are h, h - 2, and h - 16

by Pythagoras ___ h^2 = (h - 2)^2 + (h - 16)^2

h^2 = h^2 - 4h + 4 + h^2 - 32h + 256 ___ 0 = h^2 - 36h + 260

factoring ___ 0 = (h - 26)(h - 10)

h equals 26 and 10 ___ but 10 is not long enough to be 16" longer than anything

h = 26 ___ h - 2 = 24 ___ h - 16 = 10
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