two sides of a right triangle are 20 cm and 21 cm find the third side?

If the third side (X) is the hypotenuse then length of X is sqrt(20^2+21^2)

If the hypotenuse is the side 21 cm long then length of the third side = sqrt(21^2-20^2)

Ciao from Rome S

What you want to do to solve this equation is to use the Pythagorean Theorem, which states the squared length of the hypotenuse of a right triangle is equal to the sum of the square of the base plus the square of the height, mathematically it looks like this a^2+b^2=c^2

1) substitute a and b for 20 cm and 21 cm which looks like this: 20^2+21^2=c^2

2) square both the numbers to get 400+441=c^2

3) add the two numbers together to get 841=c^2

4) take the square root of each side in order to reduce c^2 to just plain c, which looks like this: √841=c and the square root of 841 is 29 so the length of the third side of the triangle is 29.

Hope this helps

Because it is a right triangle, the Pythagorean Theorem tells us that a^2 + b^2 = c^2 where c is the hypotenuse and a & b are the legs. For the values given, either 20 & 21 are the legs in which case the hypotenuse is sqrt (20^2 + 21^2) = 29, or 21 is the hypotenuse in which case the other leg is 6.4.

They are probably looking for 29 as the answer.

29

a^2 + b^2 = c^2

I'm assuming that 20 and 21 are A and B, and you want to find the hypotenuse, or C.

(20)^2 + (21)^2 = c^2

400 + 441 = c^2

841 = c^2

c = 29

Your answer can't be found, because your question is not clear.

Suppose, three sides of right angle triangle are h, p and b.

If your h=21cm,

p=20cm, then let the value obtained for b=x cm.

In second case if

b=21cm, p=20cm, then the value obtained for h, will not have the same value as you have obtained in previous case for b, hence as you don't have cleared which side length is given, thair will not be any perfact length of third side.

you use the Pythagorean Equation: a²+b²=c², where a and b are the sides and c is the hypotenuse.

so 20² + 21² = c²

400 + 441 = c²

29 = c

If the two sides are adjacent to the right angle, then the third side is the hypotenuse.

h² = 20² + 21²

h = √841

Trust Me "king" Arthur, you CAN just KNOW the answer

(but I do agree you can work it out with a^2+b^2=c^2)

As I kid my students, memorize these it "will make you faster

smarter and better looking like me"

Read below............they are worth learning...........I PROMISE

PYTHAGOREAN TRIPLES...........(sets of three numbers that always make a RIGHT TRIANGLE

The first few are::::::

3...4...5

5...12...13

7...24...25

8...15...17....................try one................8^2+15^2=17^2

..................................................................64+225=289

........................................................................289=289

9...40...41

11..60..61

20..21..29********************************HERE IS YOUR PROBLEM

.

.

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There are MANY more but ALSO multiples of these work

3^2+4^2=5^2

...9+15=25

.......25=25

MULITIPLY BY 5..................3*5.......4*5........5*5

................................................15........20.........25

15^2+20^2=25^2

225+400=625

........625=625

NOW LASTLY (Miss Smiles says thank goodness he is going to be quiet and go away)

MULTIPLY ........BY.........******17********

3*17.....4*17.....5*17.............................Now look at your problem and ITS ANSWER

51..........68.........85

If you want to spend a little time CREATING triples do the following

ALWAYS make M greater than N and use these expressions

M.......N..............M^2-N^2.............2*M*N...................M^2+N^2

2.........1

3.........1

3.........2

4.........1

4.........2

4.........3.............4^2-3^2................2*4*3.....................4^2+3^2

............................16-9......................24..........................16+9

...............................7.........................24............................25.......remember that one from above

5.........1

5.........2

5.........3

5.........4

6.........1etc.

The third side must be greater than 1 and less than 41. You did not state anything about where these side lengths lie in the triangle, therefore that is the best answer that can be given.