ANSWER
Length of the shorter leg: 3 m
Length of the longer leg: 4 m
EXPLANATION
Let the length of the longer leg be x.
First, let us make a sketch of the problem:
We can find the value of x by applying the Pythagoras rule:
[tex]a^2+b^2=c^2[/tex]where c = length of the hypotenuse
a, b = length of the other two legs
Hence, we have that:
[tex]\begin{gathered} x^2+(x-1)^2=5^2 \\ x^2+x^2-2x+1=25 \\ 2x^2-2x+1-25=0 \\ 2x^2-2x-24=0 \end{gathered}[/tex]Solve for x by factorizing:
[tex]\begin{gathered} 2x^2-8x+6x-24=0 \\ 2x(x-4)+6(x-4)=0 \\ (2x+6)+(x-4)=0 \\ 2x=-6;x-4=0 \\ x=\frac{-6}{2}=-3;x=4 \end{gathered}[/tex]Since the length of the leg of a triangle cannot be negative, we have that:
[tex]x=4m[/tex]Hence, the length of the shorter leg is:
[tex]\begin{gathered} 4-1 \\ \Rightarrow3m \end{gathered}[/tex]Therefore, the length of the shorter leg is 3 m and the length of the longer leg is 4 m.
