Question

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Answer 1

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 $b$ inches and the perpendicular be $p$ inches.

From Pythagoras theorem :

The hypotenuse (h) $=\sqrt{p^2+b^2}$

Plugging the values to find the hypotenuse.

$h=\sqrt{p^2+b^2}=\sqrt{4^2+6^2}=\sqrt{16+36}=\sqrt{52}$

Note:If a square root is not a perfect square, then it is considered an irrational number.

And $\sqrt{52}=7.211$ 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.