The lengths of two sides of a right triangle are 5 inches and 8 inches. What is the difference between the two possiblelengths of the third side of the triangle? Round your answer to the nearest tenth. 3.1 inches3.2 inches10.0 inches15.7 inches

Answer:Option 2 - 3.2 inches.                       Step-by-step explanation:Given : The lengths of two sides of a right triangle are 5 inches and 8 inches.To find : What is the difference between the two possible  lengths of the third side of the triangle? Solution : According to question, it is a right angle triangle Applying Pythagoras theorem,[tex]H^2=P^2+B^2[/tex]Where, H is the hypotenuse the longer side of the triangleP is the perpendicularB is the baseAssume that H=8 inches and B = 5 inchesSubstitute the value in the formula,[tex]8^2=P^2+5^2[/tex][tex]64=P^2+25[/tex][tex]P^2=64-25[/tex][tex]P^2=39[/tex][tex]P=\sqrt{39}[/tex][tex]P=6.24[/tex]Assume that P=8 inches and B = 5 inchesSubstitute the value in the formula,[tex]H^2=8^2+5^2[/tex][tex]H^2=64+25[/tex][tex]H^2=89[/tex][tex]H=\sqrt{89}[/tex][tex]H=9.43[/tex]Therefore, The possible length of the third side of the triangle is [tex]L=H-P[/tex][tex]L=9.43-6.24[/tex][tex]L=3.19[/tex]Therefore, The difference between the two possible  lengths of the third side of the triangle is 3.2 inches.So, Option 2 is correct.