Solve the proportion for the variable given.

4/6 = 9/x
A) 10
B) 6
C) 1
D) 27/2

D

Step-by-step explanation:

4/6 = 9/X

2/3 = 9/X

X = 9 × 3/2

X = 27/2

addition

step-by-step explanation:

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