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If EFGH is an isosceles trapezoid , EH = 4x-27, FG = x + 9 , EG = 3y + 19 and FH=11y-21, solve for x and y.

Sagot :

AtomOOFidn

Answer: X = 12, Y = 5

Step-by-step explanation:

4x-27 = x+9

   +27      +27

4x = x + 36

-x     -x

3x = 36

3x/3 = 36/3

X = 12

3y + 19 = 11y - 21

     +21          +21

3y + 40 = 11y

-3y           -3y

40 = 8y

40/8 = 8y/8

Y = 5

MrRoyalidn

The values of x and y are 12 and 5, respectively

The given parameters are:

  • EH = 4x-27
  • FG = x + 9
  • EG = 3y + 19
  • FH= 11y - 21

The slant sides of an isosceles trapezoid are equal.

So, we have:

[tex]EH =FG[/tex]

This gives

[tex]4x - 27 = x + 9[/tex]

Collect like terms

[tex]4x - x = 27 + 9[/tex]

[tex]3x = 36[/tex]

Divide through by 3

[tex]x = 12[/tex]

Also, the diagonals of an isosceles trapezoid are equal.

So, we have:

[tex]EG = FH[/tex]

This gives

[tex]3y + 19 = 11y - 21[/tex]

Collect like terms

[tex]11y - 3y =19 + 21[/tex]

[tex]8y = 40[/tex]

Divide through by 8

[tex]y = 5[/tex]

Hence, the values of x and y are 12 and 5, respectively

Read more about isosceles trapezoid at:

https://brainly.com/question/10187910

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