The difference between the two possible lengths of the third side of the triangle is:
3.2 inches
The lengths of two sides of a right triangle are 5 inches and 8 inches.
This means that the third side could be the hypotenuse of the triangle or it could be a leg of a triangle with hypotenuse as: 8 inches.
Let the third side be denoted by c.
Then by using the Pythagorean Theorem we have:
[tex]c^2=5^2+8^2\\\\i.e.\\\\c^2=25+64\\\\i.e.\\\\c^2=89\\\\i.e.\\\\c=9.434\ inches[/tex]
[tex]8^2=c^2+5^2\\\\i.e.\\\\64=c^2+25\\\\i.e.\\\\c^2=64-25\\\\i.e.\\\\c^2=39\\\\i.e.\\\\c=\sqrt{39}\\\\i.e.\\\\c=6.245\ inches[/tex]
Hence, the difference between the two possible lengths of the third side is:
[tex]=9.434-6.245\\\\=3.189\ inches[/tex]
which to the nearest tenth is: 3.2 inches
Answer:
B) 3.2 inches
Step-by-step explanation:
did it on edge
