For what values of x and y is quadrilateral ABCD a parallelogram

The value of x is 6 and y is 3.

Given that,

ABCD is a parallelogram in which sides of parallelogram are,

AB = 8x- 34, BC = 6x- 4

CD = 9x-40, AD = 4y+20

We have to find,

The value of x and y in a quadrilateral ABCD ?

According to the question,

By the property of a parallelogram,

The opposite sides of a parallelogram are equal and parallel to each other.

AD = BC

CD = AB

Substitute the values of AD and BC and solve for the value of x and y,

And

Substitute the value of x in equation 1,

Hence, The value of x is 6 and y is 3.

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Option (A)

Step-by-step explanation:

By the property of a parallelogram,

Opposite sides of a parallelogram are equal and parallel to each other.

AD = BC and DC = AB

9x - 40 = 8x - 34

9x - 8x = 40 - 34

x = 6

4y + 20 = 6x - 4

4y - 6x = -24

2y - 3x = -12

Now we will substitute the value of x,

2y = 3x - 12

2y = 3(6) - 12

2y = 6

y = 3

Therefore, Option (A) will be the correct option.

283 square feet

step-by-step explanation:

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