The length of the shortest side = 5m
Explanations:The longest side of the triangle is the hypotenuse
Longest side = 13 m
One of the shorter sides is 7m longer than the other
Therefore, the two short sides are x and x+7
where x represents the shortest side
Using the Pythagora's theorem.
The square of the longest side equals the sum of the squares of the two short sides
[tex]\begin{gathered} 13^2=x^2+(x+7)^2 \\ 169=x^2+x^2\text{ + 14x + 49} \\ 2x^2\text{ + 14x }-120\text{ = 0} \\ x^2\text{ + 7x - 60 = 0} \\ \text{Solving the quadratic equation above} \\ x\text{ = 5, -12} \\ \text{The sidelength cannot be negative} \end{gathered}[/tex]The shortest side length = x = 5m
