In rectangle FGHJ , the diagonals intersect at point M, FM = 3.2x , and JG = 40. What is the value of x?
Enter your answer as a decimal in the box.

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

14.29%

step-by-step explanation:

this is a good question! i’ll do some research and what i find, i’ll contact you asap when i have something! ✊