DSQ: Calculating the perimeter of a quadrilateral - GMAT Quantitative Reasoning
Card 0 of 4
What is the perimeter of Rhombus 
?
Statement 1: 
has perimeter 
.
Statement 2: 
is equilateral.
What is the perimeter of Rhombus
Statement 1:
Statement 2:
Each diagonal divides Rhombus 
into two triangles, both isosceles.
Statement 1 alone establishes the perimeter of one such triangle. However, it does not make it clear what equal side lengths 
and 
and diagonal length 
are. For example, 
fits the perimeter, but so does 
.
Statement 2 alone gives no information about the actual lengths of the sides.
Assume both statements are true. Since 
is equilateral, 
. It follows that 
, and 
. Also, the diagonals of a rhombus bisect their angles and are each other's perpendicular bisectors, so the rhombus, with their diagonals, is given below.
has perimeter 
, which means that
Since 
is known to be a 
triangle, the proportions of the side lengths are known; along with the above equation, 
, and, subsequently, the perimeter, can be determined.
Each diagonal divides Rhombus
Statement 1 alone establishes the perimeter of one such triangle. However, it does not make it clear what equal side lengths
Statement 2 alone gives no information about the actual lengths of the sides.
Assume both statements are true. Since
Since
Compare your answer with the correct one above
What is the perimeter of quadrilateral 
?
(1) Diagonal 
and
are perpendicular with midpoint 
.
(2) 
What is the perimeter of quadrilateral
(1) Diagonal
(2)
To find the perimeter of the quadrilateral, we need to know whether it is of a special type of quadrilaterals and we need to know the length of the sides.
Statement 1 tells us only that the quadrilateral is a rhombus. Indeed, a quadrilateral with perpendicular diagonals intersecting at their midpoint must be a rhombus. However we don't know any length of the sides.
Statement 2 says gives us the length us two consecutive sides. It could be tempting to answer that it is sufficient, however, we can't conclude that the quadrilateral has equal lengths. Therefore this statement alone is insufficient.
Both statements together are sufficient since we can conclude that the quadrilateral is a rhombus, and twice 
will give us the perimeter.
To find the perimeter of the quadrilateral, we need to know whether it is of a special type of quadrilaterals and we need to know the length of the sides.
Statement 1 tells us only that the quadrilateral is a rhombus. Indeed, a quadrilateral with perpendicular diagonals intersecting at their midpoint must be a rhombus. However we don't know any length of the sides.
Statement 2 says gives us the length us two consecutive sides. It could be tempting to answer that it is sufficient, however, we can't conclude that the quadrilateral has equal lengths. Therefore this statement alone is insufficient.
Both statements together are sufficient since we can conclude that the quadrilateral is a rhombus, and twice
Compare your answer with the correct one above
Consider rectangle 
.
I) Side 
is three fourths of side 
.
II) Side 
is 
meters long.
What is the perimeter of 
?
Consider rectangle
I) Side
II) Side
What is the perimeter of
To find perimeter, we need to find the length of all the sides. Recall that rectangles are made up of two pairs of equal sides.
I) Relates one side to another non-equivalent side.
II) Gives us side 
, which must be equivalent to 
.
Use II) and I) to find all the side lengths, then add them up. Both are needed.
Recap:
Consider rectangle CONT
I) Side CO is three fourths of side ON
II) Side NT is 15.7 meters long
What is the perimeter of CONT?
Because we are dealing with a rectangle, we know the following:
Find perimeter with:
Use I) and II) to write the following equation:
So:
And finally:
To find perimeter, we need to find the length of all the sides. Recall that rectangles are made up of two pairs of equal sides.
I) Relates one side to another non-equivalent side.
II) Gives us side
Use II) and I) to find all the side lengths, then add them up. Both are needed.
Recap:
Consider rectangle CONT
I) Side CO is three fourths of side ON
II) Side NT is 15.7 meters long
What is the perimeter of CONT?
Because we are dealing with a rectangle, we know the following:
Find perimeter with:
Use I) and II) to write the following equation:
So:
And finally:
Compare your answer with the correct one above
Find the perimeter of the rectangle.
Statement 1: The area of the rectangle is 24.
Statement 2: The diagonal of the rectangle is 5.
Find the perimeter of the rectangle.
Statement 1: The area of the rectangle is 24.
Statement 2: The diagonal of the rectangle is 5.
Statement 1): The area of the rectangle is 24.
Write the area for a rectangle and substitute the value of the area.
The length and width of the rectangle are unknown, and each set of dimensions will provide a different perimeter. This statement is insufficient to find the perimeter of the rectangle.
Statement 2): The diagonal of the rectangle is 5.
Given the diagonal of the rectangle, the Pythagorean Theorem can be used to solve for the diagonal. Express the equation in terms of length and width.
Similar to the case in Statement 1), both the length and width are unknown, and the equation by itself is insufficient to solve for the perimeter of the rectangle.
Attempting to use both equations: and to solve for length and width will yield complex numbers as part of the solution.
Therefore:
Statement 1): The area of the rectangle is 24.
Write the area for a rectangle and substitute the value of the area.
The length and width of the rectangle are unknown, and each set of dimensions will provide a different perimeter. This statement is insufficient to find the perimeter of the rectangle.
Statement 2): The diagonal of the rectangle is 5.
Given the diagonal of the rectangle, the Pythagorean Theorem can be used to solve for the diagonal. Express the equation in terms of length and width.
Similar to the case in Statement 1), both the length and width are unknown, and the equation by itself is insufficient to solve for the perimeter of the rectangle.
Attempting to use both equations:
Therefore:
Compare your answer with the correct one above