Question

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

Answer 1

Answer:

Option J 13

Step-by-step 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