Question

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

Answer 1

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

Answer 2

Answer: B. 164

The value of y =30

The value of CD = 164

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
`AC = 7y - 30` and
`BD = 4y + 60`

`\Rightarrow\ 7y-30=4y+60\\\\\Rightarrow\ 7y-4y=60+30\\\\\Rightarrow\ 3y=90\\\\\Rightarrow\ y=30`

The value of CD =
`5(30)+14=150+14=164`