Rectangles - ISEE Middle Level Quantitative Reasoning
Card 0 of 20
Using the information given in each question, compare the quantity in Column A to the quantity in Column B.
A certain rectangle is seven times as long as it is wide.
Column A Column B
the rectangle's the rectangle's
perimeter area
(in units) (in square units)
Using the information given in each question, compare the quantity in Column A to the quantity in Column B.
A certain rectangle is seven times as long as it is wide.
Column A Column B
the rectangle's the rectangle's
perimeter area
(in units) (in square units)
This type of problem reminds us to be wary of simply plugging in numbers (which works with certain problems). If you were to choose 1 and 7 here, the perimeter would be larger; if you chose 10 and 70, the area would be much larger.
To solve this problem with variables:
From here we can see that smaller values of 
will lead to a larger perimeter, while larger values of 
will lead to a larger area.
The answer cannot be determined.
This type of problem reminds us to be wary of simply plugging in numbers (which works with certain problems). If you were to choose 1 and 7 here, the perimeter would be larger; if you chose 10 and 70, the area would be much larger.
To solve this problem with variables:
From here we can see that smaller values of
The answer cannot be determined.
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If the length of a rectangle is twice the width, and the width is three inches, what is the area of the rectangle?
If the length of a rectangle is twice the width, and the width is three inches, what is the area of the rectangle?
In order to find the area of a rectangle we use the formula 
.
In this problem, we know the width is 
. We also know that the length is twice as long as the width, which can be written as 
. This means that in order to find the length, we must multiply the width by 
.
Now that we know that our length is 
, we simply multiply it by our width of 
.
The area of the rectangle is 
.
In order to find the area of a rectangle we use the formula
In this problem, we know the width is
Now that we know that our length is
The area of the rectangle is
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Which is the greater quantity?
(a) The surface area of a rectangular prism with length 60 centimeters, width 30 centimeters, and height 15 centimeters
(b) The surface area of a cube with sidelength 300 millimeters
Which is the greater quantity?
(a) The surface area of a rectangular prism with length 60 centimeters, width 30 centimeters, and height 15 centimeters
(b) The surface area of a cube with sidelength 300 millimeters
(a) The surface of a rectangular prism comprises six rectangles, so we can take the sum of their areas.
Two rectangles have area: 
.
Two rectangles have area: 
.
Two rectangles have area: 
.
Add the areas: 
(b) The surface of a cube comprises six squares, so we can square the sidelength - which we rewrite as 30 centimeters - and multiply the result by 6:
.
The first figure has the greater surface area.
(a) The surface of a rectangular prism comprises six rectangles, so we can take the sum of their areas.
Two rectangles have area:
Two rectangles have area:
Two rectangles have area:
Add the areas:
(b) The surface of a cube comprises six squares, so we can square the sidelength - which we rewrite as 30 centimeters - and multiply the result by 6:
The first figure has the greater surface area.
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Column A Column B
The area of a The area of a square
rectangle with sides with sides 7cm.
11 cm and 5 cm.
Column A Column B
The area of a The area of a square
rectangle with sides with sides 7cm.
11 cm and 5 cm.
First, you must calculate Column A. The formula for the area of a rectangle is 
. Plug in the values given to get 
, which gives you 
. Then, calculate the area of the square. Since all of the sides of a square are equal, the formula is 
, or 
. Therefore, the area of the square is 
, which gives you 
. Therefore, the quantity in Column A is greater.
First, you must calculate Column A. The formula for the area of a rectangle is
Compare your answer with the correct one above
What is the length of a rectangular room with an area of 
and a width of 
What is the length of a rectangular room with an area of
We have the area and the width, so we can plug those values into our equation and solve for our unknown.
We have the area and the width, so we can plug those values into our equation and solve for our unknown.
Compare your answer with the correct one above
What is the length of a rectangular room with an area of 
and a width of 
What is the length of a rectangular room with an area of
We have the area and the width, so we can plug those values into our equation and solve for our unknown.
We have the area and the width, so we can plug those values into our equation and solve for our unknown.
Compare your answer with the correct one above
What is the length of a rectangular room with an area of 
and a width of 
What is the length of a rectangular room with an area of
We have the area and the width, so we can plug those values into our equation and solve for our unknown.
We have the area and the width, so we can plug those values into our equation and solve for our unknown.
Compare your answer with the correct one above
What is the length of a rectangular room with an area of 
and a width of 
What is the length of a rectangular room with an area of
We have the area and the width, so we can plug those values into our equation and solve for our unknown.
We have the area and the width, so we can plug those values into our equation and solve for our unknown.
Compare your answer with the correct one above
What is the length of a rectangular room with an area of 
and a width of 
What is the length of a rectangular room with an area of
We have the area and the width, so we can plug those values into our equation and solve for our unknown.
We have the area and the width, so we can plug those values into our equation and solve for our unknown.
Compare your answer with the correct one above
What is the length of a rectangular room with an area of 
and a width of 
What is the length of a rectangular room with an area of
We have the area and the width, so we can plug those values into our equation and solve for our unknown.
We have the area and the width, so we can plug those values into our equation and solve for our unknown.
Compare your answer with the correct one above
What is the length of a rectangular room with an area of 
and a width of 
What is the length of a rectangular room with an area of
We have the area and the width, so we can plug those values into our equation and solve for our unknown.
We have the area and the width, so we can plug those values into our equation and solve for our unknown.
Compare your answer with the correct one above
What is the length of a rectangular room with an area of 
and a width of 
What is the length of a rectangular room with an area of
We have the area and the width, so we can plug those values into our equation and solve for our unknown.
We have the area and the width, so we can plug those values into our equation and solve for our unknown.
Compare your answer with the correct one above
What is the length of a rectangular room with an area of 
and a width of 
What is the length of a rectangular room with an area of
We have the area and the width, so we can plug those values into our equation and solve for our unknown.
We have the area and the width, so we can plug those values into our equation and solve for our unknown.
Compare your answer with the correct one above
What is the length of a rectangular room with an area of 
and a width of 
What is the length of a rectangular room with an area of
We have the area and the width, so we can plug those values into our equation and solve for our unknown.
We have the area and the width, so we can plug those values into our equation and solve for our unknown.
Compare your answer with the correct one above
What is the length of a rectangular room with an area of 
and a width of 
What is the length of a rectangular room with an area of
We have the area and the width, so we can plug those values into our equation and solve for our unknown.
We have the area and the width, so we can plug those values into our equation and solve for our unknown.
Compare your answer with the correct one above
What is the length of a rectangular room with an area of 
and a width of 
What is the length of a rectangular room with an area of
We have the area and the width, so we can plug those values into our equation and solve for our unknown.
We have the area and the width, so we can plug those values into our equation and solve for our unknown.
Compare your answer with the correct one above
What is the length of a rectangular room with an area of 
and a width of 
What is the length of a rectangular room with an area of
We have the area and the width, so we can plug those values into our equation and solve for our unknown.
We have the area and the width, so we can plug those values into our equation and solve for our unknown.
Compare your answer with the correct one above
What is the length of a rectangular room with an area of 
and a width of 
What is the length of a rectangular room with an area of
We have the area and the width, so we can plug those values into our equation and solve for our unknown.
We have the area and the width, so we can plug those values into our equation and solve for our unknown.
Compare your answer with the correct one above
What is the length of a rectangular room with an area of 
and a width of 
What is the length of a rectangular room with an area of
We have the area and the width, so we can plug those values into our equation and solve for our unknown.
We have the area and the width, so we can plug those values into our equation and solve for our unknown.
Compare your answer with the correct one above
What is the length of a rectangular room with an area of 
and a width of 
What is the length of a rectangular room with an area of
We have the area and the width, so we can plug those values into our equation and solve for our unknown.
We have the area and the width, so we can plug those values into our equation and solve for our unknown.
Compare your answer with the correct one above