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

###### Question:

## Answers

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

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.

29

Step-by-step explanation:

[tex](20,21,x) \\Pythagoras -Theorem =\\a^2+b^2 = c^2\\\\20^2 + 21^2 = x^2\\400 + 441 = x^2\\841 = x^2\\Square -root-both-sides\\\sqrt{841} = \sqrt{x^2} \\29 = x\\\\x = 29[/tex]

5 times g EQ so the answer is 29

[tex]\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2} \qquad \begin{cases} c=\stackrel{hypotenuse}{x}\\ a=\stackrel{adjacent}{20}\\ b=\stackrel{opposite}{21}\\ \end{cases} \\\\\\ x=\sqrt{20^2+21^2}\implies x=\sqrt{841}\implies x=29[/tex]

a² + b² = c²

20² + 21² = c²

400 + 441 = c²

c² = 841

c = √841

c = 29

B. 29

Step-by-step explanation:

Use Pythagoras theorem.

a² + b² = c²

x is the hypotenuse.

20² + 21² = x²

400 + 441 = x²

841 = x²

√841 = √(x²)

29 = x

check the picture below.

[tex]What is the length of the hypotenuse,x,if (20,21,x) is a pythogorean triple?[/tex]

I can confirm that, B, 29, is without a doubt, the correct answer.

Step-by-step explanation:

Hello, by definition a perfect square can be written as [tex]a^2[/tex] where a in a positive integer.

So, to answer the first question, [tex]6^2[/tex] is a perfect square.

(a,b,c) is a Pythagorean triple means the following

[tex]a^2+b^2=c^2[/tex]

Here, it means that

[tex]x^2=20^2+21^2=841=29^2 \ \ \ so\\\\x=29[/tex]

Thank you.