Question 869894
clearly this triangle belongs to the 5-12-13 family or right triangles, but if this is not apparent...

We are given that

{{{l=w+7}}}

substituting into the Pythagorean formula



{{{w^2+(w+7)^2=13^2}}}

which can be solved to obtain

{{{w=-12}}} or {{{w=5}}}

but since this is geometry we know all measurements are positive. 

{{{w=5in}}}

this in turn means

{{{l=12in}}}