Question 952453
b=long leg; a=short leg=(0.5b)-11ft; c=hypotenuse=b+1
{{{a^2+b^2=c^2}}} Substitute for a and c, solve for b
{{{.25b^2-11b+121+b^2=b^2+2b+1}}}
{{{1.25b^2-11b+121=b^2+2b+1}}}Subtract{{{(b^2+2b+1)}}} from each side.
{{{0.25b^2-13b+120=0}}}*[invoke quadratic "b", 0.25, -13, 120 ]
b=40 or b=12 (long leg)
For b=40:
a=0.5b-11ft=0.5(40)-11 ft=9 ft (short leg)
c=b+1=40ft+1 ft=41 ft(hypotenuse)
For b=12
a=.5(12)-11 ft=6-11=-5ft does not work
ANSWER 1: The long leg is 40 feet.
ANSWER 2: The short leg is 9 feet.
ANSWER 3: The hypotenuse is 41 feet.
CHECK:
{{{a^2+b^2=c^2}}}
{{{(9 ft)^2+(40 ft)^2=(41 ft)^2}}}
{{{81ft^2+1600ft^2=1681ft^2}}}
{{{1681ft^2=1681ft^2}}}