Question

Which side length will form an obtuse triangle with side lengths 8 and 10

Answer 1

Option J 13

Explanation:

we know that

If applying the Pythagoras Theorem

`c^(2)> a^(2) +b^(2)` ----> is an obtuse triangle

`c^(2)< a^(2) +b^(2)` ----> is an acute triangle

`c^(2)= a^(2) +b^(2)` ----> is a right triangle

where

c is the greater side

Verify each case

case F) we have

`c=10, a=6, b=8`

substitute

`10^(2)> 6^(2) +8^(2)`

`100> 100` -----> is not true

Is a right triangle

case G) we have

`c=10, a=9, b=8`

substitute

`10^(2)> 9^(2) +8^(2)`

`100> 145` -----> is not true

Is an acute triangle

case H) we have

`c=12, a=8, b=10`

substitute

`12^(2)> 8^(2) +10^(2)`

`144> 164` -----> is not true

Is an acute triangle

case J) we have

`c=13, a=8, b=10`

substitute

`13^(2)> 8^(2) +10^(2)`

`169> 164` -----> is true

Is an obtuse triangle