Question

the diagonals of rectangle nopq intersect at point r. if qr=3x-4 and np=5x+20, solve for x.

Answer 1

The diagonals of a rectangle are congruent.  We have half of diagonal QO and the whole diagonal of NP.  So the equation will look like this: 5x+20=2(3x-4).  5x+20=2(3x-4).  5x + 20 = 6x - 8.  28 = x.  Therefore, x = 28 and the length of the diagonals is 160