Trapezoid RSTV had median UK. If VT= #4x-6# and UK = #3x+2# and RS = #x+12#, find #x#?

Answer 1

James Atkins

#x=2#

The median of any trapezoid is equal to the average of the bases.

The average of the bases can also be written as the sum of the bases over two.

Thus, since the bases are #VT# and #RS#, and the median #UK#,

#(VT+RS)/2=UK#

Substitute in the lengths.

#((4x-6)+(x+12))/2=3x+2#

Multiply both sides by #2#.

#4x-6+x+12=6x+4#

Simplify.

#5x+6=6x+4#

#x=2#

We can check by plugging in #2#.

#VT=2# #UK=8# #RS=14#

#8# indeed is the average of #2# and #14#, so #x=2#.

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Answer 2

Savannah Aguilar

In a trapezoid with median ( UK ), the lengths of the diagonals are equal. Thus, ( VT = RS ). Equating ( VT ) and ( RS ), we have:

[ 4x - 6 = x + 12 ]

Solving for ( x ):

[ 4x - x = 12 + 6 ] [ 3x = 18 ] [ x = 6 ]

Therefore, ( x = 6 ).

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