Application: a rhombus as an area of 72 ft and the product of the diagonals is 144. what is the length of each diagonal?

(other info: the information was missing something so here is an explanation on how to finish it, i don't get what it is, so maybe you can me!

it's just a different way to apply the formula:
a= ½ *(b1+b2)*h
a=32
b1+b2 = 16
plug those values into the equation and solve for h)

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4