What is the perimeter of quadrilateral Q?

(1) Q is a rectangle.
(2) The area of Q is 25.

OA=E

Source: Princeton Review

Hi Vjesus12.

The perimeter of the quadrilateral Q is given by \(p= w+x+y+z \), where \(w, x, y, z\) are the lengths of each side of the quadrilateral.

Statement 1:

(1) Q is a rectangle.

Since Q is a rectangle, then we have that \( w=y\) and \( x=z\), so the perimeter is \(p= 2x+2y\), but we don't know the values of \(x\) and \(y\). Hence, this statement is NOT SUFFICIENT.

Statement 2:

(2) The area of Q is 25.

Now, we don't know what type of quadrilateral Q is. So, we can't get anything from the area. Therefore, this statement is NOT SUFFICIENT.

Statement 1 and Statement 2:

If Q is a rectangle with area equal to 25, we can get several cases, for example,

(i) Q is a square of side 5, then the perimeter of Q is 20.
(ii) Q is a rectangle with sides 25/2 and 2 respectively, therefore the perimeter of Q is 29.

Since we've got two different answers then we conclude that using both statements is NOT SUFFICIENT.

In conclusion, the correct answer is the option _E_.

I hope it helps.