The length of a rectangle is 7 inches more than its width. A diagonal of the rectangle is 13 inches long. What is the length and width of the rectangle?

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

We are given that

substituting into the Pythagorean formula:


 

which can be solved to obtain 

 or  

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

this in turn means