DSQ: Calculating the length of the diagonal of a rectangle - GMAT Quantitative Reasoning
Card 0 of 5
What is the length of the diagonal of rectangle 
?
(1) 
(2) 
and 
What is the length of the diagonal of rectangle
(1)
(2)
In order to find the diagonal, we must know the sides of the rectangle or know whether the triangles ADC or ABD have special angles.
Statement 1 alone doesn't let us calculate the hypothenuse of the triangles, because we only know one side.
Statement 2 alone is sufficient because it allows us to find all angles of the triangles inside of the rectangle. We can see that they are special triangles with angles 30-60-90. Any triangle with these angles will have its sides in ratio 
, where 
is a constant. Here, 
, knowing this, we can calculate the length of the hypothenuse, also the diagonal, which will be 
.
Hence, statement 2 is sufficient.
In order to find the diagonal, we must know the sides of the rectangle or know whether the triangles ADC or ABD have special angles.
Statement 1 alone doesn't let us calculate the hypothenuse of the triangles, because we only know one side.
Statement 2 alone is sufficient because it allows us to find all angles of the triangles inside of the rectangle. We can see that they are special triangles with angles 30-60-90. Any triangle with these angles will have its sides in ratio
Hence, statement 2 is sufficient.
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Rectangle 
has a perimeter of 
, what is its area?
I) The diagonal of 
is 
inches.
II) The length of one side is 
inches.
Rectangle
I) The diagonal of
II) The length of one side is
I) Gives us the length of ASOF's diagonal. This by itself does not give us any way of finding the other sides.
II) Gives us one side length. From there we can use the perimeter to find the other side length and then the area.
Therefore, Statement II is sufficient to answer the question.
I) Gives us the length of ASOF's diagonal. This by itself does not give us any way of finding the other sides.
II) Gives us one side length. From there we can use the perimeter to find the other side length and then the area.
Therefore, Statement II is sufficient to answer the question.
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Rectangle 
, has diagonal 
. What is the length of 
?
(1) Angle 
.
(2) 
.
Rectangle
(1) Angle
(2)
The length of a diagonal of a rectangle can be calculated like a hypotenuse using the Pythagorean Theorem provided we have information about the lengths of the rectangle.
Statement 1 tells us that both triangles ADC and ABD have their angles in ratio 
, which means that their sides will have length in ratio 
, where 
is a constant. We can't tell however what length the diagonal will be.
Statment 2 tells us that side AC is 1. From there we can't conclude anything. Indeed, rectangle ABCD might as well be a square or a very thin rectangle, we don't know.
Both statements together however, allow us to tell that 
and therefore that the diagonal will be 2.
Hence, both statements together are sufficient.
The length of a diagonal of a rectangle can be calculated like a hypotenuse using the Pythagorean Theorem provided we have information about the lengths of the rectangle.
Statement 1 tells us that both triangles ADC and ABD have their angles in ratio
Statment 2 tells us that side AC is 1. From there we can't conclude anything. Indeed, rectangle ABCD might as well be a square or a very thin rectangle, we don't know.
Both statements together however, allow us to tell that
Hence, both statements together are sufficient.
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is a rectangle. What is the ratio 
?
(1) 
.
(2) 
.
(1)
(2)
To solve this, we need information about the lengths of the sides or to whether triangles ADB and ACD are special triangles.
Statement 1 tells us that CDA has length 3. This is not enough and we still don't know whether the rectangle is of a special type of rectangle.
Statement 2 tells us that triangles ADB and ACD are special triangles, indeed, they have their angles in ratio 
. That means that their sides will be in ratio 
. Now we don't need to know what is constant 
, since it will cancel out in the ratio.
Therefore, statement 2 alone is sufficient.
To solve this, we need information about the lengths of the sides or to whether triangles ADB and ACD are special triangles.
Statement 1 tells us that CDA has length 3. This is not enough and we still don't know whether the rectangle is of a special type of rectangle.
Statement 2 tells us that triangles ADB and ACD are special triangles, indeed, they have their angles in ratio
Therefore, statement 2 alone is sufficient.
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Find the diagonal of rectangle 
.
I) The area of 
is 
.
II) The perimeter of 
is 
.
Find the diagonal of rectangle
I) The area of
II) The perimeter of
In order to find the diagonal of a rectangle we need the length of both sides.
We can't find the lengths with just the area or just the perimeter, but by using them both together we can make a small system of equations with two unknowns and two equations.
Then we can solve for each side and use the Pythagorean Theorem to find our diagonal.
In order to find the diagonal of a rectangle we need the length of both sides.
We can't find the lengths with just the area or just the perimeter, but by using them both together we can make a small system of equations with two unknowns and two equations.
Then we can solve for each side and use the Pythagorean Theorem to find our diagonal.
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