SOLUTION: the diagonal of a rectangle is 6cm longer than its base. Its height is 10 cm more than one-third of its base. Find the dimension of the resctangle.

Let b=base

Let h=height

Let d=diagonal



Given:

d = b+6

h = (b/3)+10



By Pythagorean theorem:





Substitute the givens to get one eqn w/one unknown:





Expand (and cancel one  from each side):





Multiply both sides  by 9:





Bring it all over to one side:





  --->  b = 24  --> h = 18,  d = 30





Check:

 =  = 900

  (ok!)