Given
The hypotenuse is given 85 feet long.
The long leg of a right triangle is 71 feet longer than the short leg.
Explanation
Let the longer leg be x and short leg be y.
Then the relation obtained is
[tex]x=71+y[/tex]
Then the figure obtained is
Now apply the Pythagoras theorem,
[tex]\begin{gathered} 85^2=x^2+y^2 \\ 85^2=(y+71)^2+y^2 \\ 7225=y^2+5041+142y+y^2 \\ 7225-5041=142y+2y^2 \\ 2184=142y+2y^2 \\ 2y^2+142y-2184=0 \\ (y-13)(y+84)=0 \\ y=13,-84 \end{gathered}[/tex]
The value of y cannot be negative,hence the value of y obtained is 13.
Now find the value of x.
[tex]\begin{gathered} x=71+y \\ x=71+13 \\ x=84 \end{gathered}[/tex]
Answer
Hence the length of shorter leg is 13 feet.
The length of longer leg is 84 feet.
