Answer: No,it is not possible to have a right triangle where the lengths of the legs are whole numbers and the length of the hypotenuse is 23.
Step-by-step explanation:
According to the Pythagorean triplet, in a right angled triangle the hypotenuse is the longest side.
and it is given by [tex]m^2+1[/tex] and other two legs are given by [tex]m^2-1[/tex] and [tex]2m[/tex]
Now, the longest side= [tex]m^2+1=23[/tex]
[tex]\Rightarrow\ m^2=23-1\\\Rightarrow\ m^2=22[/tex]
But 22 is not a perfect square
Since [tex]4^2=16[/tex] and [tex]5^2=25[/tex], therefore the square root of 22 lies between 4 and 5.
Hence, it is not possible to have a right triangle where the lengths of the legs are whole numbers and the length of the hypotenuse is 23.
