Chapter 1 - Equations and Inequalities - Chapter 1 Test Prep - Review Exercises - Page 179: 60

$12$

Step 1. Use the figure given in the exercise and the Pythagorean Theorem, we have $(x+1)^2=(x)^2+(x-7)^2\longrightarrow x^2+2x+1=x^2+x^2-14x+49\longrightarrow x^2-16x+48=0$ Step 2. Factor the equation to get $(x-4)(x-12)=0$, thus $x=4$ and $x=12$ Step 3. Check the solutions and we find only $x=12$ fit the requirement while $x=4$ gives a negative side length.