All SSAT Upper Level Math Resources
Example Questions
Example Question #1 : How To Find The Perimeter Of A Rectangle
The length and width of a rectangle are and
. Give its perimeter in terms of
.
A rectangle has perimeter ,
the length and
the width. Substitute
and
in the perimeter formula, and simplify.
Example Question #1 : How To Find The Perimeter Of A Rectangle
A rectangle has length 30 inches and width 25 inches. Which of the following is true about its perimeter?
Its perimeter is between 9 and 10 feet.
Its perimeter is between 4 and 5 feet.
Its perimeter is between 10 and 11 feet.
Its perimeter is between 8 and 9 feet.
Its perimeter is between 5 and 6 feet.
Its perimeter is between 9 and 10 feet.
In inches, the perimeter of the rectangle can be calculated by substituting in the following formula:
The perimeter is 110 inches.
Now divide by 12 to convert to feet:
This makes the perimeter 9 feet 2 inches, which is between 9 feet and 10 feet.
Example Question #1 : How To Find The Perimeter Of A Rectangle
Perimeter of a rectangle is 36 inches. If the width of the rectangle is 3 inches less than its length, give the length and width of the rectangle.
inches
inches
inches
inches
inches
inches
Let:
The perimeter of a rectangle is , where
is the length and
is the width of the rectangle. The perimeter is known so we can set up an equation in terms of
and solve it:
So we can get:
inches
inches
Example Question #3 : How To Find The Perimeter Of A Rectangle
The length and width of a rectangle are and
, respectively. Give its perimeter in terms of
.
The perimeter of a rectangle is , where
is the length and
is the width of the rectangle. In order to find the perimeter we can substitute the
and
in the perimeter formula:
Example Question #5 : How To Find The Perimeter Of A Rectangle
The length of a rectangle is and the width of this rectangle is
meters shorter than its length. Give its perimeter in terms of
.
The length of the rectangle is known, so we can find the width in terms of :
The perimeter of a rectangle is , where
is the length and
is the width of the rectangle.
In order to find the perimeter we can substitute the and
in the perimeter formula:
Example Question #1 : How To Find The Perimeter Of A Rectangle
A rectangle has a length of inches and a width of
inches. Which of the following is true about the rectangle perimeter if
?
Its perimeter is between 7 and 8 feet.
Its perimeter is between 7.2 and 7.4 feet.
Its perimeter is between 8 and 9 feet.
Its perimeter is less than 7 feet.
Its perimeter is more than 8 feet.
Its perimeter is between 7 and 8 feet.
Substitute to get
and
:
The perimeter of a rectangle is , where
is the length and
is the width of the rectangle. So we have:
inches
Now we should divide the perimeter by 12 in order to convert to feet:
feet
So the perimeter is 7 feet and 6 inches, which is between 7 and 8 feet.
Example Question #2 : How To Find The Perimeter Of A Rectangle
Which of these polygons has the same perimeter as a rectangle with length 55 inches and width 15 inches?
The other answer choices are incorrect.
A regular hexagon with sidelength two feet
A regular octagon with sidelength two feet
A regular heptagon with sidelength two feet
A regular pentagon with sidelength two feet
The other answer choices are incorrect.
The perimeter of a rectangle is twice the sum of its length and its width; a rectangle with dimensions 55 inches and 15 inches has perimeter
inches.
All of the polygons in the choices are regular - that is, all have congruent sides - and all have sidelength two feet, or 24 inches, so we divide 140 by 24 to determine how many sides such a polygon would need to have a perimeter equal to the rectangle. However,
,
so there cannot be a regular polygon with these characteristics. All of the choices fail, so the correct response is that none are correct.
All SSAT Upper Level Math Resources
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