abcd is a rectangle. find the length of each diagonal.ac=2(5a+1) bd=2(a+1).

Question

anonymous · Answer

Because ABCD is a rectangle, we can safely infer that AB and CD are parallel, as are BC and AD.  If you draw diagonals then you get four right triangles.  (Easier to see on paper, believe me.) From there it becomes a simple matter of using the Pythagorean theorem (if you know the lengths of each side) OR simply a matter of induction: If AB = DC, then shouldn't AC = BD?  Therefore,$$2(5a+1)=2(a+1)$$Divide both sides by two,$$5a+1=a+1$$Subtract a+1 from both sides,$$4a=0$$Therefore, a=0, which because of the Pythagoream theorem, implies that the rectangle does not exist, as only $$0^2+0^2=0^2$$

anonymous · Answer

Sorry for taking so long.  Was a little confused when I got a=0 at first.  Is the equation itself incorrect?  Seems like it.

anonymous · Answer

the correct answer was 2.

anonymous · Answer

How do you figure that?  If you plug 2 into the eqns, you do not get equal sides.  You get 22=6.  How can 2 be correct?

anonymous · Answer

idk my quiz said the correct answer was 2