DSQ: Calculating the length of the side of a rectangle - GMAT Quantitative Reasoning
Card 0 of 5
Given parallelogram 
with diagonal 
. Is this parallelogram a rectangle?
-
-
Given parallelogram
The length of one diagonal alone does not prove the parallelogram to be a rectangle, nor do the lengths of the sides.
Suppose we know all of these lengths, though. Since 
is a parallelogram, if 
, then 
.
The sides 
and diagonal 
form a triangle 
with sidelengths 25, 60, and 65. The parallelogram is a rectangle if and only if 
is a right angle; therefore, we must determine whether the conditions of the Pythagorean Theorem hold:
This is true; 
is a right angle and 
is a rectangle.
Therefore, both statements together are sufficient to answer the question, but neither statement alone is sufficient to answer the question.
The length of one diagonal alone does not prove the parallelogram to be a rectangle, nor do the lengths of the sides.
Suppose we know all of these lengths, though. Since
The sides
This is true;
Therefore, both statements together are sufficient to answer the question, but neither statement alone is sufficient to answer the question.
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Ronald is making a bookshelf with a rectangular base that will be two yards tall. What is the area of the base?
I) The distance around the base will be 
yards.
II) The smaller sides of the base are half the length of the longer sides.
Ronald is making a bookshelf with a rectangular base that will be two yards tall. What is the area of the base?
I) The distance around the base will be
II) The smaller sides of the base are half the length of the longer sides.
To find the area we need the length and width of the rectangle. We can use II together with I to make an equation for perimeter with only one unknown.
So we need both to solve.
Solve for 
and then go back to find 
and then with that you can find the area of the base and you are finished.
To find the area we need the length and width of the rectangle. We can use II together with I to make an equation for perimeter with only one unknown.
So we need both to solve.
Solve for
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Find a possible width of rectangle 
.
I) 
has a perimeter of 
fathoms.
II) 
has a diagonal length of 
fathoms.
Find a possible width of rectangle
I)
II)
When asked to find the width of a rectangle we will need to use both statemests together.
For Statement I) we can use the perimeter formula.
Now, for Statement II) we will use the length of the diagonal along with the Pythagorean Theorem.
From here you can solve the perimeter equation in terms of either l or w. Then you can use substitution into the Pythagorean Theorem to solve for a possible width.
When asked to find the width of a rectangle we will need to use both statemests together.
For Statement I) we can use the perimeter formula.
Now, for Statement II) we will use the length of the diagonal along with the Pythagorean Theorem.
From here you can solve the perimeter equation in terms of either l or w. Then you can use substitution into the Pythagorean Theorem to solve for a possible width.
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A rectangle has a width measuring twice the length. Find the length.
- The rectangle has a perimeter of
.
- The rectangle's area is
.
A rectangle has a width measuring twice the length. Find the length.
- The rectangle has a perimeter of
- The rectangle's area is
Statement 1:
Recall the formula to find the perimeter of a rectangle. Substitute in the given information and solve.
Statement 2:
Recall the formula for the area of a rectangle. Substitute in the given information and solve.
Each statement alone is sufficient to answer the question.
Statement 1:
Recall the formula to find the perimeter of a rectangle. Substitute in the given information and solve.
Statement 2:
Recall the formula for the area of a rectangle. Substitute in the given information and solve.
Each statement alone is sufficient to answer the question.
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Find the length of the side of a rectangle with a width three times the length.
- The area of the rectangle is
.
- The perimeter of the rectangle is
.
Find the length of the side of a rectangle with a width three times the length.
- The area of the rectangle is
- The perimeter of the rectangle is
Statement 1: 
Statement 1 is sufficient to answer the question
Statement 2: 
Statement 2 is also sufficient to answer the question
Statement 1:
Statement 1 is sufficient to answer the question
Statement 2:
Statement 2 is also sufficient to answer the question
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