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59:26 What is the length of the hypotenuse, x, if (20, 21, x) is a Pythagorean triple? 22 29 41 42

Respuesta :

apologiabiology
if the legs are length a and b and hyptonuse is c then
a²+b²=c²

so
if the legs are 20 and 21 and the hypotnuse is x then
20²+21²=x²
400+441=x²
841=x²
29=x

Answer:  the correct option is (B) 29.

Step-by-step explanation:  We are given to find the length of the hypotenuse x, if (20, 21, x) is a Pythagorean triple.

We know that

in a right-angled triangle, the lengths of the sides (hypotenuse, perpendicular, base) is a Pythagorean triple, where

[tex]Hypotenuse^2=Perpendicular^2+base^2.[/tex]

So,  for the given Pythagorean triple, we have

[tex]x^2=20^2+21^2\\\\\Rightarrow x^2=400+441\\\\\Rightarrow x^2=841\\\\\Rightarrow x=\sqrt{841}~~~~~~~~~~~~~~~~~[\textup{taking square root on both sides}]\\\\\Rightarrow x=\pm29.[/tex]

Since the length of the hypotenuse cannot be negative, so x = 29.

Thus, the length of the hypotenuse, x = 29.

Option (B) is CORRECT.

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