Question

Can you have a right triangle where the lengths of the legs are whole numbers and the length of the hypotenuse is 23? Explain.

Answer 1

in a right angled triangle , by Pythagoras. c^2 = a^2 + b^2 where c is the hypotenuse and a and b are the 2 legs

c ^2 = 23^2 = a^2 + b^2

529 = a^2 + b^2

Answer 2

now you need to find 2 perfect square numbers which will add up to 529. Do you think there exist?

Answer 3

Idk i just need the answer so i can explain

Answer 4

He's trying to help _you_ find the answer so you _can_ explain!

Answer 5

But idk how

Answer 6

If you catn find any then we know that there are no whole numbers which fit the triangle.

Answer 7

im doing my classes online and i have no clue what im doing

Answer 8

to be honest I cant think of a quick way to do this other than to subtract square numbers from 529 and test if the result is also a square number

for example assume that one leg is 2 so the square is 4

529 - 4 = 525 Now 525 is not a square number (tested with calculator)

Answer 9

so how do i do it

Answer 10

next try 3^2 = 9
529 - 9 = 520 - nit a square
4^2 = 15
529 - 16 = 513 not a square

Answer 11

- a long process
Maybe theres a quicker way...

Answer 12

ok. im just gonna guess

Answer 13

I'm pretty sure you ca'nt have a triangle with legs = whole numbers if hypotenuse = 23.

Answer 14

A spreadsheet says @welshfella is correct, but the only explanation I know involves checking all the combinations. Good luck.

Answer 15

yea I cant think of another way either.

Answer 16

you'd have to check all square numbers up the the one after 529/2