Question

Need help!

Can the numbers 24,32,40 be the lengths of the three sides of a right triangle? Explain why or why not?

Answer 1

take the longest side - this is the 'hypotenuse'

Pythagoras' theorem states that in a right angle triangle the sum of the squares of the 2 short side is equal to the square of the long side

So square all three numbers, add the 2 smaller ones. If the sum is equal to the 3rd square then the triangle is a right angle.


Once you are familiar with this technique you might note a 'special case' - the 3 number 3,4 & 5 make up a Pythagoras triple becaus3 3^3 +4^2 = 5^2 (3+16=25)

So any triangle with side IN THE RATIO 3:4:5 will be a right angle tringle. Look at the numbers in YOUR question and see if this helps....

Answer 2

Okay

Answer 3

Correction to typos above:

take the longest side - this is the 'hypotenuse'

Pythagoras' theorem states that in a right angle triangle the sum of the squares of the 2 short side is equal to the square of the long side

So square all three numbers, add the 2 smaller ones. If the sum is equal to the 3rd square then the triangle is a right angle.


Once you are familiar with this technique you might note a 'special case' - the numbers 3,4 & 5 make up a Pythagoras triple because 3^3 +4^2 = 5^2 (9+16=25)

So any triangle with side IN THE RATIO 3:4:5 will be a right angle triangle. Look at the numbers in YOUR question and see if this helps....