Answer:
8ft
Step-by-step explanation:
Pythagorean Theorem
[tex]a^2+b^2=c^2\\\\x^2+(x+7)^2=17^2\\x^2+(x+7)(x+7)=17^2\\x^2+(x^2+7x+7x+49)=289\\2x^2+14x+49-289=289-289\\2x^2+14x-240=0\\[/tex]
Use Quadratic Formula to Solve
[tex]\frac{-b+-\sqrt{b^2-4ac} }{2a} \\\frac{-14+-\sqrt{14^2-4(2)(-240)} }{2(2)} \\\frac{-14+-\sqrt{2116} }{4}\\x=\frac{-14+46}{4}, x=\frac{-14-46}{4}\\x=8, -15[/tex]
Ignore negative sign
Shorter side is 8ft and longer one is 15ft
