Which set of numbers could represent the lengths of the sides of a right triangle?
9, 10, 11
16, 32, 36
8, 12, 16
3, 4, 5
3,4,5
using a^2 +b^2 = c^2 plug in any of the numbers i plugged in
3^2 +4^2 which gave me 9+16 and that is 25 and 5^2 is 25
Answer:
3, 4, 5
Step-by-step explanation:
We are given the sets of numbers and we are supposed to find Which set of numbers could represent the lengths of the sides of a right triangle
So, we need to use Pythagoras theorem
\(Hypotenuse^{2} =Perpendicular^{2} +Base^{2}\)
1) 9,10,11
Hypotenuse = 11
So, using Pythagoras theorem
\(11^{2} =10^{2} +9^{2}\)
\(121=100 +81\)
\(121 eq 181\)
Since the given set does not satisfy the Pythagoras theorem.So, the given set of number could not represent the lengths of the sides of a right triangle.
2)16, 32, 36
Hypotenuse = 36
So, using Pythagoras theorem
\(36^{2} =32^{2} +16^{2}\)
\(1296=1024 +256\)
\(1296 eq 1280\)
Since the given set does not satisfy the Pythagoras theorem.So, the given set of number could not represent the lengths of the sides of a right triangle.
3)8, 12, 16
Hypotenuse = 36
So, using Pythagoras theorem
\(16^{2} =12^{2} +8^{2}\)
\(256=144 +64\)
\(256 eq 208\)
Since the given set does not satisfy the Pythagoras theorem.So, the given set of number could not represent the lengths of the sides of a right triangle.
4)3, 4, 5
Hypotenuse = 5
So, using Pythagoras theorem
\(5^{2} =4^{2} +3^{2}\)
\(25=16 +9\)
\(25\=25\)
Since the given set satisfy the Pythagoras theorem.So, the given set of number could represent the lengths of the sides of a right triangle.
Hence 3, 4, 5 is the set of numbers could represent the lengths of the sides of a right triangle