Question

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

Answer 1

No you can't because a right angle is 90

Answer 2

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

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.