DSQ: Calculating the perimeter of a rectangle - GMAT Quantitative Reasoning
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What is the perimeter of rectangle 
?
(1) The area of 
is 81
(2) Side 
What is the perimeter of rectangle
(1) The area of
(2) Side
To know the perimeter of a rectangle, we need to know length and width.
Statement (1) provides Area, which does not provide the necessary information. NOT SUFFICIENT
Statement(2) provides one side, but we still need the other to determine perimeter. NOT SUFFICIENT.
Both together are sufficent however since if we know one side and the area, we can find the remaining side using division, and then use the two side lengths to find the perimeter.
To know the perimeter of a rectangle, we need to know length and width.
Statement (1) provides Area, which does not provide the necessary information. NOT SUFFICIENT
Statement(2) provides one side, but we still need the other to determine perimeter. NOT SUFFICIENT.
Both together are sufficent however since if we know one side and the area, we can find the remaining side using division, and then use the two side lengths to find the perimeter.
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You are given a square and a rectangle. Which has the greater perimeter?
Statement 1: The length of the rectangle is twice the sidelength of the square,
Statement 2: The width of the rectangle is half the sidelength of the square.
You are given a square and a rectangle. Which has the greater perimeter?
Statement 1: The length of the rectangle is twice the sidelength of the square,
Statement 2: The width of the rectangle is half the sidelength of the square.
Let 
be the sidelength of the square. Then its perimeter is 
.
From Statement 1 alone, the length of the rectangle is 
, and, if 
is the width, the perimeter of the rectangle is 
. Therefore, we can prove that the rectangle has the greater perimeter.
From Statement 2 alone, the width of the rectangle is 
, and its perimeter is at least 
- but unless we know the length, we do not know whether the total perimeter is greater than, equal to, or less than 
.
Let
From Statement 1 alone, the length of the rectangle is
From Statement 2 alone, the width of the rectangle is
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The table in a hall has a length of 
feet. What is its perimeter?
I) The tabletop is exactly two and a half feet above the floor.
II) The area of the table is four times three more than the width.
The table in a hall has a length of
I) The tabletop is exactly two and a half feet above the floor.
II) The area of the table is four times three more than the width.
To find perimeter we need length and width. We are given the length.
I) Is irrelevant.
II) We are given a way of relating area and width. Since we know that area is length times width, we can use II to set up an equation where we substitute in the known length along with the given statement to solve for our width
Solve the second one for w and you're good to go!
.
Therefore the perimeter would be:
To find perimeter we need length and width. We are given the length.
I) Is irrelevant.
II) We are given a way of relating area and width. Since we know that area is length times width, we can use II to set up an equation where we substitute in the known length along with the given statement to solve for our width
Solve the second one for w and you're good to go!
Therefore the perimeter would be:
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Farmer Jeff Jenkins is making a new rectangular field for his goats and needs to know how much fencing he needs to buy.
I) The goats will need at least 
square yards to roam.
II) One edge of the field will be 
yards long and will be made up of a river.
Farmer Jeff Jenkins is making a new rectangular field for his goats and needs to know how much fencing he needs to buy.
I) The goats will need at least
II) One edge of the field will be
To find perimeter, we need the lengths of both sides.
I) Gives us the area, which gives us one equation and two unknowns. Alone this statement is not sufficient.
II) Gives us one side length of the field.
We can use this with I) to find the other side length.
Once we have both sides, we can find perimeter easily.
Thus the perimeter is,
.
To find perimeter, we need the lengths of both sides.
I) Gives us the area, which gives us one equation and two unknowns. Alone this statement is not sufficient.
II) Gives us one side length of the field.
We can use this with I) to find the other side length.
Once we have both sides, we can find perimeter easily.
Thus the perimeter is,
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What is the perimeter of the rectangle?
- The area is
.
- The width measures
.
What is the perimeter of the rectangle?
- The area is
- The width measures
Statement 1: Although the area is given, we need more information in order to answer the question.
but this can means our dimenions are 
or 
Statement 2: We're told the width measures 
which means our dimensions are 
.
Using BOTH statements, we can find the perimeter: 
Statement 1: Although the area is given, we need more information in order to answer the question.
Statement 2: We're told the width measures
Using BOTH statements, we can find the perimeter:
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True or false: 
Statement 1: A rectangle with length 
and width 
has area greater than 100.
Statement 2: A rectangle with length 
and width 
has perimeter greater than 100.
True or false:
Statement 1: A rectangle with length
Statement 2: A rectangle with length
Statement 1 alone provides insufficient information. For example:
Case 1: 
The area of a rectangle with these dimensions is their product, which is 120; this exceeds 100.
Case 2: 
The area of a rectangle with these dimensions is their product, which is 480; this exceeds 100.
Assume Statement 2 alone. The perimeter of a rectangle is twice the sum of their dimensions, so
, answering the question in the affirmative.
Statement 1 alone provides insufficient information. For example:
Case 1:
The area of a rectangle with these dimensions is their product, which is 120; this exceeds 100.
Case 2:
The area of a rectangle with these dimensions is their product, which is 480; this exceeds 100.
Assume Statement 2 alone. The perimeter of a rectangle is twice the sum of their dimensions, so
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