SSAT Upper Level Math : How to find the perimeter of a rectangle

Study concepts, example questions & explanations for SSAT Upper Level Math

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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 .

Possible Answers:

Correct answer:

Explanation:

A rectangle has perimeter  the length and  the width. Substitute  and  in the perimeter formula, and simplify.

Example Question #2 : 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?

Possible Answers:

Its perimeter is between 5 and 6 feet.

Its perimeter is between 8 and 9 feet.

Its perimeter is between 4 and 5 feet.

Its perimeter is between 9 and 10 feet.

Its perimeter is between 10 and 11 feet.

Correct answer:

Its perimeter is between 9 and 10 feet.

Explanation:

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 #3 : 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.

Possible Answers:

 inches

 inches

 inches

 inches

inches

Correct answer:

inches

Explanation:

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 #4 : How To Find The Perimeter Of A Rectangle

The length and width of a rectangle are  and , respectively. Give its perimeter in terms of .

Possible Answers:

Correct answer:

Explanation:

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 .

Possible Answers:

Correct answer:

Explanation:

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 #6 : 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 ?

Possible Answers:

Its perimeter is less than 7 feet.

Its perimeter is between 7 and 8 feet.

Its perimeter is between 7.2 and 7.4 feet.

Its perimeter is more than 8 feet.

Its perimeter is between 8 and 9 feet.

Correct answer:

Its perimeter is between 7 and 8 feet.

Explanation:

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 #7 : 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?

Possible Answers:

A regular hexagon with sidelength two feet

The other answer choices are incorrect.

A regular pentagon with sidelength two feet

A regular octagon with sidelength two feet

A regular heptagon with sidelength two feet

Correct answer:

The other answer choices are incorrect.

Explanation:

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.

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