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Trapezoid NSMK with midsegment HG is shown, where MG = 18, GS=-32-y. HG = 24, NS = 62, and KM = −y+12
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Complete the statements.
The value of z is [DROP DOWN 1] and the value of y is [DROP DOWN 2].
Drop Down 1
Select a Value
DROP DOWN 2
Select a Value

Trapezoid NSMK with midsegment HG is shown where MG 18 GS32y HG 24 NS 62 and KM y12 S K G M Complete the statements The value of z is DROP DOWN 1 and the value class=


Answer :

semsee45

Answer:

x = 2

y = -24

Step-by-step explanation:

The midsegment of a trapezoid connects the midpoints of its non-parallel sides, and is parallel to the parallel bases.

We are given trapezoid NSMJ with midsegment HG, where:

  • MG = 18
  • GS = -3x - y
  • HG = 24
  • NS = 6x
  • KM = -y + 12

The length of the midsegment of a trapezoid is half of the sum of the lengths of the two parallel bases. Given that NS and KM are the parallel bases, then:

[tex]HG=\dfrac{NS+KM}{2}\\\\\\24=\dfrac{6x-y + 12}{2}\\\\\\48=6x-y+12\\\\\\y=6x+12-48\\\\\\y=6x-36[/tex]

As point G is the midpoint of side MS then:

[tex]MG = GS\\\\18=-3x-y[/tex]

Rearrange to isolate y:

[tex]y=-3x-18[/tex]

We have now created a system of two linear equations:

[tex]\begin{cases} y=6x-36\\y=-3x-18\end{cases}[/tex]

Substitute the first equation into the second equation and solve for x:

[tex]6x-36=-3x-18\\\\6x-36+3x=-3x-18+3x\\\\9x-36=-18\\\\9x-36+36=-18+36\\\\9x=18\\\\x=2[/tex]

Therefore, the value of x is:

[tex]\Large\boxed{\boxed{x = 2}}[/tex]

To find the value of y, we can substitute x = 2 into either of the equations for y. Let's use y = 6x - 36:

[tex]y = 6(2) - 36\\\\y=12-36\\\\y=-24[/tex]

Therefore, the value of y is:

[tex]\Large\boxed{\boxed{y=-24}}[/tex]

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