SOLUTION: The length of the sides of a triangle are 5cm, 9cm and 13cm. What is the equal length that should be added to the sides so we would get a right triangle? Thanks in advance.

Question 311690: The length of the sides of a triangle are 5cm, 9cm and 13cm. What is the equal length that should be added to the sides so we would get a right triangle?
Thanks in advance.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The length of the sides of a triangle are 5cm, 9cm and 13cm.
What is the equal length that should be added to the sides so we would get a right triangle?
:
Using a^2 + b^2 = c^2
:
Let x = length added to each side to make it a right triangle
(x+5)^2 + (x+9)^2 = (x+13)^2
FOIL
x^2 + 10x + 25 + x^2 + 18x + 81 = x^2 + 26x + 169
combine like terms on the left
x^2 + x^2 - x^2 + 10x + 18x - 26x + 25 + 81 - 169 = 0
Results
x^2 + 2x - 63 = 0
Factors to
(x+9)(x-7) = 0
the positive solution
x = 7 added to each side to make this a right triangle
:
:
Check
12^2 + 16^2 = 20^2
144 + 256 = 400
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