# In parallelogram EFGH with perimeter 52, find EG (the diagonal)and y on the other diagonal.     How do I solve this problem? I'm really confused especially with the square root  of 153 part!...

In parallelogram EFGH with perimeter 52, find EG (the diagonal)and y on the other diagonal.

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durbanville | Certified Educator

Understanding the properties of a parallelogram will help you to solve this problem. I will answer the section you are having trouble with (the square root) and the question about the other diagonal as they are closely related questions but eNotes rules prevent me from answering the remaining question.

The diagonals of a parallelogram bisect each other. We will call the  centre `O`

1. `therefore EO = OG = sqrt153`  and
2. `and FO = OH therefore 3y-10 = y`

Therefore to find EG `= 2times sqrt153 OR sqrt153 + sqrt153`

`therefore = 2(sqrt153)` `= 24.74` (rounded off to 2 decimals or in surd form simplify the contents of the square root which is

3 x 3 x 17:

`= 2(sqrt(3^2 times 17))`

`= 6sqrt17`

To solve the other diagonal we have created an equation to solve:

`3y - 10 = y`

`therefore 3y-y = 10`

`therefore 2y = 10`

`therefore y=5`

therefore diagonal EG = 24.78 units or `6sqrt17`  and y (on diagonal FH) = 5 units.