Answer:
The question is:
Is the length of the hypotenuse a rational number?
No the hypotenuse is not a rational number.
Step-by-step explanation:
We have been given a right angled triangle.
Where the base and perpendicular lengths were given.
Let the base be [tex]b[/tex] inches and the perpendicular be [tex]p[/tex] inches.
From Pythagoras theorem :
The hypotenuse (h) [tex]=\sqrt{p^2+b^2}[/tex]
Plugging the values to find the hypotenuse.
[tex]h=\sqrt{p^2+b^2}=\sqrt{4^2+6^2}=\sqrt{16+36}=\sqrt{52}[/tex]
Note:If a square root is not a perfect square, then it is considered an irrational number.
And [tex]\sqrt{52}=7.211[/tex] so it is not a perfect square as it has decimals and its an irrational number.
The length of the hypotenuse is not a rational number instead its an irrational term.
