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

10 answers
Question:

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

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.

Similar Solved Works

4 answers

Một vật có khối lượng m = 200 g dao động điều hòa theo phương trình x=10sin(4\pi+\frac{/pi}{3} ) (cm) . Năng lượng cần thiết để vật dao động là...
3 answers

What is the importance of culture​

What is the importance of culture​...
3 answers

Find the missing side lengths in each pair of similar figures. ABC - XYZ

Find the missing side lengths in each pair of similar figures. ABC - XYZ [tex]Find the missing side lengths in each pair of similar figures. ABC - XYZ[/tex]...
3 answers

Draw an area model and then solve using the standard algorithm 27x36=

Draw an area model and then solve using the standard algorithm 27x36=...
3 answers

This is what I say to the young Jewish boy wondering what I have done with his years. It is in his name that I speak to you and

This is what I say to the young Jewish boy wondering what I have done with his years. It is in his name that I speak to you and that I express to you my deepest gratitude. No one is as capable of gratitude as one who has emerged from the kingdom of night. We know that every moment is a moment of gra...
3 answers

In twenty years, kayleen will be four times older than she is today. what is her current

In twenty years, kayleen will be four times older than she is today. what is her current age?...
4 answers

Rosa represents her school as -2, because it is two blocks south of her house. Yesterday, Rosa left school and walked either north

Rosa represents her school as -2, because it is two blocks south of her house. Yesterday, Rosa left school and walked either north or south to a friend's house. If she walked four blocks, which values could represent where she ended up? Select all that apply....
4 answers

This is a pattern for a function

This is a pattern for a function...
4 answers

Jaymie wants to construct congruent angles with a compass and straightedge, while Annie wants to construct congruent segments

Jaymie wants to construct congruent angles with a compass and straightedge, while Annie wants to construct congruent segments with a compass and straightedge. Describe the similarities and differences between their construction steps....
6 answers

What is the measure of the angles in the triangle shown below.​

What is the measure of the angles in the triangle shown below.​ [tex]What is the measure of the angles in the triangle shown below.​[/tex]...
3 answers

What other lifeways emerged besides being a h-g or a farmer (agriculturalist)?

What other lifeways emerged besides being a h-g or a farmer (agriculturalist)?...
5 answers

Simplify3[23+(4−2)3−(6−2[2]]]3[23+(4-2)3-(6-2[2]

Simplify 3 [ 2 3 + ( 4 − 2 ) 3 − ( 6 − 2 [ 2 ] ] ] 3 [ 2 3 + ( 4 - 2 ) 3 - ( 6 - 2 [ 2 ]...
4 answers

A cup contains 500 g water initially at a temperature of 100oC. This cup is put in a largeroom of temperature of 20oC.a/ What will be

A cup contains 500 g water initially at a temperature of 100oC. This cup is put in a large room of temperature of 20oC. a/ What will be the temperature of the water if the cup stays in the room for a long time? Explain your answer. b/ Compute the change of entropy of the system water – room, know...
3 answers

List of Stereotypes of Christian religion

List of Stereotypes of Christian religion...
4 answers

How did George Washington keep the continental army together at valley forge?

How did George Washington keep the continental army together at valley forge?...
4 answers

The diameter of a circular CD is 120 millimeters. Which of the following is closest to the circumference of the CD in millimeters?O

The diameter of a circular CD is 120 millimeters. Which of the following is closest to the circumference of the CD in millimeters? O 376.8 mm 0753.6 mm O 11,304 mm O 45,216 mm...
10 answers

What is the circumference of a round pizza with an area of 36 square inches ? step by step like can anyone explain to me in words

What is the circumference of a round pizza with an area of 36 square inches ? step by step like can anyone explain to me in words...
3 answers

What is the slope? simplify your answer and write it as a proper fraction, improper fraction, integer​

What is the slope? simplify your answer and write it as a proper fraction, improper fraction, integer​ [tex]What is the slope? simplify your answer and write it as a proper fraction,improper fraction,integer​[/tex]...
3 answers

How much time is required for an airplane to reach its takeoff speed of 77m/s if it starts from rest

how much time is required for an airplane to reach its takeoff speed of 77m/s if it starts from rest to average acceleration is 8.2 m/s (to the power of 2)...
3 answers

What rights did german citizens loose under the natzis?​

What rights did german citizens loose under the natzis?​...

-- 0.020782--