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ABCD is an isosceles trapezoid with diagonals that intersect at point P. If AB || CD , AC = 7y – 30, BD = 4y + 60, and CD = 5y + 14, solve for y


A. 124
B. 164
C. 180
D. 292

Respuesta :

I think its A or B not sure(educated guess)
JeanaShupp

Answer:  B. 164

The value of y =30

The value of CD = 164

Step-by-step explanation:

Properties of isosceles trapezoid:

  • Two sides are parallel.
  • The opposite non-parallel sides are equal.
  • The diagonals are equal.

Given: ABCD is an isosceles trapezoid with diagonals that intersect at point P.  AB || CD

⇒ BC= AD [opposite non-parallel sides]

AC=BD  [ Diagonals are equal]

Since [tex]AC = 7y - 30[/tex] and [tex]BD = 4y + 60[/tex]

[tex]\Rightarrow\ 7y-30=4y+60\\\\\Rightarrow\ 7y-4y=60+30\\\\\Rightarrow\ 3y=90\\\\\Rightarrow\ y=30[/tex]

The value of CD = [tex]5(30)+14=150+14=164[/tex]