GRE Math : How to find the length of the diagonal of a rectangle
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Example Questions
Example Question #1 : How To Find The Length Of The Diagonal Of A Rectangle
Given Rectangle ABCD.
Quantity A: The length of diagonal AC times the length of diagonal BD
Quantity B: The square of half of ABCD's perimeter
Quantity A is greater.
Quantity B is greater.
The relationship cannot be determined from the information given.
The two quantities are equal.
Quantity B is greater.
Suppose ABCD has sides a and b.
The length of one of ABCD's diagonals is given by a2+ b2 = c2, where c is one of the diagonals.
Note that both diagonals are of the same length.
Quantity A: The length of diagonal AC times the length of diagonal BD
This is c * c = c2.
Quantity A = c2 = a2+ b2
Now for Quantity B, remember that the perimeter of a rectangle with sides a and b is Perimeter = 2(a + b).
Half of Perimeter = (a + b)
Square Half of Perimeter = (a + b)2
Use FOIL: (a + b)2 = a2+ 2ab + b2
Quantity B = (a + b)2 = a2+ 2ab + b2
The question is asking us to compare a2+ b2 with a2+ 2ab + b2.
Note that as long as a and b are positive numbers (in this case a and b are dimensions of a rectangle, so they must be positive), the second quantity will be greater.
Example Question #2 : How To Find The Length Of The Diagonal Of A Rectangle
If rectangle 
Lets call our longer side L and our shorter side W.
If the perimeter is equal to 68, then
We also have that
If we then plug this into our equation for perimeter, we get 
Therefore, 
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