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

Accepted Solution

Answer:Option J 13Step-by-step explanation:we know thatIf applying the Pythagoras Theorem[tex]c^{2}> a^{2} +b^{2}[/tex] ----> is  an obtuse triangle[tex]c^{2}< a^{2} +b^{2}[/tex] ----> is  an acute triangle[tex]c^{2}= a^{2} +b^{2}[/tex] ----> is a right trianglewherec is the greater sideVerify each casecase F) we have[tex]c=10, a=6, b=8[/tex]substitute[tex]10^{2}> 6^{2} +8^{2}[/tex][tex]100> 100[/tex] -----> is not trueIs a right trianglecase G) we have[tex]c=10, a=9, b=8[/tex]substitute[tex]10^{2}> 9^{2} +8^{2}[/tex][tex]100> 145[/tex] -----> is not trueIs an acute trianglecase H) we have[tex]c=12, a=8, b=10[/tex]substitute[tex]12^{2}> 8^{2} +10^{2}[/tex][tex]144> 164[/tex] -----> is not trueIs an acute trianglecase J) we have[tex]c=13, a=8, b=10[/tex]substitute[tex]13^{2}> 8^{2} +10^{2}[/tex][tex]169> 164[/tex] -----> is trueIs an obtuse triangle