Solution:
Given that,
The lengths of two sides of a right triangle are 5 inches and 8 inches
Let the sides of the triangle are:
a = 5
b = 8
c = x
Case 1:
Let the third side be hypotenuse
By pythogoras theorem,
[tex]c^2=a^2+b^2[/tex]
Therefore,
[tex]x^2 = 5^2+8^2\\\\x^2 = 25+64\\\\x^2 = 89\\\\x = 9.433( consider\ positive\ value)[/tex]
So, first possible value of the third side is 9.433 inches
Case 2
Let 8 inches is the hypotenuse of the triangle
Therefore,
[tex]8^2 = x^2+5^2\\\\64 = x^2+25\\\\x^2 = 64-25\\\\\x^2 = 39\\\\x = 6.245[/tex]
What is the difference between the two possible lengths of the third side of the triangle
Difference = 9.433 - 6.245 = 3.188
[tex]Difference \approx 3.2[/tex]
Thus the difference between the two possible lengths of the third side of the triangle is 3.2 inches