Find the value of x and y for which the quadrilateral is a parallelogram. Show your solution and explain. (Need answer today pls)

Question

Answer 1

Hello Beaux;

We can use the similarity between the upper and below triangles as they have

48 : (3x - 6) = (2y - 23) : (y + 1) Order is imprtant

Let's simplify the left ratio by 3.

16 2y - 23

_____ = ______. ==> Cross multiplication ==> 16y + 16 = 2xy - 4y - 23x + 46 ==> 20y + 23x - 2xy = 30

(x - 2) y + 1

We need one more equation, that diagonals are equal in length

48 + 3x - 6 = y + 1 + 2y - 23

3y - 3x = 64

y - x = 64/3 ==> y = x + 64/3

Let's substitute into first one equation. 20y + 23x - 2xy = 30

20(x + 64/3) + 23x - 2x(x + 64/3) = 30

20x + 1280/3 + 23x -2x² - 128/3 = 90/3

2x² - 43x - 1062/3 = 0

This has two solutions as (x = 55.5 and x = -12.5 but we can get the first one, no negative for length)

So; x = 55.5, then y = x + 64/3 ==> y = (359.5)/3 ≅ 119.8 ≈ 120

Numbers are not that friendly. I hope I could be of help.

Answer 2

I already answered the same type of question earlier.

Please see that problem and use the result from it.