Question

the measure of pair of adjacent sides of a parallelogram are 15cm and 20cm.if the length of one diagonals is 25cm find the area of the parallelogram.

Answer 1

well, let's try the 20 on the bottom and the 15 sloping up toward the right. Try the diagonal connecting the two right ends.
draw altitude h
that divides the base into x and (20-x)
x^2+ h^2 = 225 so h^2 = 225-x^2
(20-x)^2 + h^2 = 625
-----------------------

400 -40 x + x^2 +(225-x^2)=625

that gives x = 0 so try the 25 as the long diagonal

x^2+h^2 = 225 again
but
(x+20)^2 + h^2 = 625
x^2 + 40 x +400 + 225-x^2 = 625
40 x = again

so we have to bite the bullet and let x = 0
That means that our parallelogram is a RECTANGLE
area = 20*15 = 300 cm^2
:)
(if we were smart we would have noticed that we had a 3,4,5 right triangle )