Question

Could the three given values be a,b, and c in triangle ABC? [Select yes or no]

Answer 1

We have a right triangle so we need to use the Pythagorean theorem in order to know if the values given could be in triangle ABC.

The Pythagorean theorem is

`c^2=a^2+b^2`

for

a=3

b=4

c=5

`a^2+b^2=3^2+4^2=25`

`c^2=5^2=25`

It is a right triangle because we satisfy the Pythagorean theorem

For

a=10

b=8

c=6

`a^2+b^2=10^2+8^2=164`

`c^2=6^2=36`

The results are not equal therefore it is not a right triangle

For

a=5

b=12

c=13

`a^2+b^2=5^2+12^2=169`
`c^2=13^2=169`

It is a right triangle because we satisfy the Pythagorean theorem

For

a=1

b=1

c=2

`a^2+b^2=1^2+1^2=2`
`c^2=2^2=4`

The results are not equal therefore it is not a right triangle