Can you have a right triangle where the lengths of the legs are whole numbers and the length of the hypotenuse is 23? Explain.

Question

asked Mar 7, 2018 3.2k views

1 Answer

Azzy · Answer 1 · 2018-03-12T00:57:42+0000

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.

Explanation:

According to the Pythagorean triplet, in a right angled triangle the hypotenuse is the longest side.

and it is given by
m^2+1 and other two legs are given by
m^2-1 and

Now, the longest side=
m^2+1=23

$\Rightarrow\ m^2=23-1\\\Rightarrow\ m^2=22$

But 22 is not a perfect square

Since
4^2=16 and
5^2=25 , 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.