Question

Which set of numbers could represent the lengths of the sides of a right triangle?

Answer 1

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

$11^{2} =10^{2} +9^{2}$

$121=100 +81$

$121\neq 181$

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

$36^{2} =32^{2} +16^{2}$

$1296=1024 +256$

$1296\neq 1280$

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

$16^{2} =12^{2} +8^{2}$

$256=144 +64$

$256\neq 208$

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

Answer 2

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