Find WX and show work

Given:

In a parallelogram WXYZ, WX=4x+5 and YZ= 7x-22.

To find:

The WX.

Solution:

In parallelogram WXYZ,

            [Opposite sides of a parallelogram are equal]

Putting the given values, we get

Isolating variable terms.

Divide both sides by -3.

Now,

Putting x=9, we get

Therefore, the value of WX is 41.

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