The length of one side of a right triangle is shown in this diagram.What could be the lengths of the two remaining sides of the triangle?A. 6 inches and 12 inchesB. 10 inches and 12 inchesC.15 inches and 17 inchesD. 16 inches and 25 inches

Step 1
Given; The length of one side of a right triangle is shown in this diagram.
What could be the lengths of the two remaining sides of the triangle?
Step 2
Euclidean geometry, For a right-angled triangle, the sum of the square of the two shorter sides of a right triangle is equal to the third side, which is the longest; in symbols,
[tex]a^2=b^2+c^2[/tex]From the image; Using the Pythagoras theorem we have that
[tex]\begin{gathered} a^2-b^2=8^2 \\ where\text{ a=longest side or hypotenuse} \\ b=other\text{ unknown side} \end{gathered}[/tex][tex]\begin{gathered} Checking\text{ the options;} \\ 17^2-15^2=64 \end{gathered}[/tex][tex]64=8^2[/tex]Thus the answer is;
[tex]15\text{ inches and 17inches}[/tex]