Answer:
Let the unknown length be x
We have a formula to find the triplet of a right angle triangle
Put the given length equal to all three terms in the triplet
[tex]2m,m^2-1,m^2+1[/tex]
put 16 equal to all above three but number comes out has to be integer.
[tex]2m=16[/tex]
[tex]\Rightarrow m=8[/tex]
Now, [tex]m^2-1=16[/tex]
[tex]m^2=17[/tex] will not give integer.
And now, [tex]m^2+1=16[/tex]
[tex]m^2=15[/tex] will not get integer value
Hence, the value of m will be 8
And substituting the value in the triplet formula we get
[tex]2m=2\cdot 8=16[/tex] which is given.
[tex]m^2-1=64-1=63[/tex] the other leg and is odd.
And [tex]m^2+1=64+1=65[/tex] the hypotenuse or the longest side.
Hence, 16,63 and 65 will form a right triangle
Pythagoras theorem is:
[tex]\text{one side}^2+\text{other side}^2=hypotenuse^2[/tex]
Here, 16 and 63 are sides or legs and 65 is the hypotenuse.
