We want to obtain the length of the hypotenuse.
But we must obtain x first.
Since this is a right-angle triangle, we must employ Pythagoras Theorem;
[tex](x+10)^2=10^2+(9x)^2[/tex]
The square of the hypotenuse is equal to the sum of the square of the other two sides, let's expand the equation, we obtain;
[tex]\begin{gathered} x^2+20x+100=100+81x^2 \\ \text{collect like terms to obtain} \\ 81x^2-x^2-20x+100-100=0 \\ 80x^2-20x=0 \\ 80x^2=20x \\ \text{divide both sides by 20x} \\ 4x=1 \\ x=\frac{1}{4}\text{ } \end{gathered}[/tex]
Thus, the length of the hypotenuse is
[tex]10\frac{1}{4}\text{ inches}[/tex]
