Answered

IDNLearn.com is your go-to platform for finding reliable answers quickly. Join our community to receive prompt and reliable responses to your questions from knowledgeable professionals.

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

Thank you for contributing to our discussion. Don't forget to check back for new answers. Keep asking, answering, and sharing useful information. IDNLearn.com has the solutions to your questions. Thanks for stopping by, and see you next time for more reliable information.