Question 952766
Since the triangle is right triangle you can use the Pythagorean theorem to find the lengths of each side {{{a^2+b^2=c^2}}} where {{{c}}} is the hypotenuse and {{{a}}} and {{{b}}} are the lengths of the sides.


The longest side of every right triangle is the hypotenuse so right away we know that {{{c=13}}}.


To calculate the sides you need to make separate equations.  One side is {{{a=x}}} and the other is {{{b=7+a}}}. This is because it says "One of the shorter sides is 7 m longer than the other" which can be translated into the equation {{{7+x}}} which leaves the remaining side as simply {{{x}}}.


Plug these equations into the Pythagorean Theorem. 
{{{c=13}}} 
{{{a=x}}} 
{{{b=7+x}}}


{{{a^2+b^2=c^2}}}
{{{x^2+(7+x)^2=13^2}}}
Distribute then solve for x to find the shortest side.
{{{x^2+x^2+14x+49=169}}}
{{{2x^2+14x-120=0}}}
{{{x^2+7x-60=0}}}
{{{x+12)(x-5)=0}}}
{{{x=-12}}} {{{x=5}}}
The value is 5 because a length cannot be negative.