Answer
7 feet
Work Step by Step
$x^2+(x+8)^2=20^2$
$x^2+x^2+8x+8x+8*8=400$
$2x^2+16x+64=400$
$(2x^2+16x+64=400)/2$
$x^2+8x+32=200$
$x^2+8x-168=0$
$x=(-b±\sqrt {b^2-4ac} )/2a$
$x=(-8±\sqrt {8^2-4*1*-168} )/2*1$
$x=(-8±\sqrt {64+4*1*168})/2$
$x=(-8±\sqrt {64+672})/2$
$x=(-8±\sqrt {736})/2$
$x=(-8±\sqrt {720+16})/2$
$x=(-8±\sqrt {180*4+4*4})/2$
$x=(-8±\sqrt {184*4})/2$
$x=(-8±2\sqrt {184})/2$
$x=(-4±\sqrt {184})$
We are talking about distance, so we can't have a negative distance. Thus, we want the positive square root.
$x=-4+\sqrt {184}$
$x=-4+13.56$
$x=9.565$
$9.565+9.565+8-20$
$19.13+8-20$
$27.13-20$
$7.13$
