Basic Geometry : Plane Geometry

Study concepts, example questions & explanations for Basic Geometry

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Example Questions

Example Question #61 : Quadrilaterals

Find the perimeter of a rectangle given length 7 and width 2.

Possible Answers:

Correct answer:

Explanation:

To solve, simply use the formula for the perimeter of a rectangle. Thus,

If the formula escapes you, simply draw a picture and add all of the sides together. Rememeber, a rectangle has 4 sides, two are equal and the other 2 are equal.

Example Question #52 : How To Find The Perimeter Of A Rectangle

A rectangle has an area of . The rectangle's sides have values of cm and cm. What is the perimeter of the rectangle?

Possible Answers:

Correct answer:

Explanation:

First, we must solve for . The formula for the area of a rectangle is . Because we know the area is , and the length and width are  and , we can plug these in to solve for , as follows:

Since we know that , we can use this to solve for the sides of the rectangle:

and

We can now use these values to solve for the rectangle's perimeter:

Therefore, the perimeter of the rectangle is .

Example Question #52 : How To Find The Perimeter Of A Rectangle

A rectangle has an area of . What is the perimeter of the rectangle?

Possible Answers:

Not enough information is given. 

Correct answer:

Not enough information is given. 

Explanation:

Not enough information is given to solve this problem. While  is a possible answer (assuming all of the sides of the rectangle are ), because it is a rectangle, you cannot assume that all of the sides are the same. Because  is not a prime number, there is more than one combination of numbers that could work out to equal an area of 

Example Question #51 : How To Find The Perimeter Of A Rectangle

 

Horton's Tile and Fixtures cuts Spanish tile in a rectangular shape that is wide and has an area of . What would be the perimeter of a cut Spanish tile?

Possible Answers:

Correct answer:

Explanation:

Since we know the width and area, we can determine the length by using the equation for area of a rectangle:

Now that we know the length of the tile, we can solve for perimeter:

Example Question #55 : How To Find The Perimeter Of A Rectangle

If the length of a rectangle is 2 inches longer than the width, and the width is  , what is the perimeter of the rectangle?

Possible Answers:

Correct answer:

Explanation:

First we need to know that the square root of 4 is 2, we can know this because because if we work backwards we see that 2 x 2= 4, so we know the width of the rectangle is 2.

 

Since the length is 2 more than the width, we add 2 + 2 and get a length of 4 inches.

 

Now we can draw the rectangle and label each width (short side) with a measure of 2 inches and each length (long side) with a measure of 4 inches.

Now all we need to do is add up all the sides, so we have 2 + 2 + 4 + 4 which equals 12.

 

Since we are adding, and the measurements are in inches, our answer is .

Example Question #62 : Quadrilaterals

The rectangle below has a perimeter of 54. Find the lengths of the unknown side. That is, find S.

Rectangle_7-20

Possible Answers:

17

7

3

11

5

Correct answer:

7

Explanation:

For a rectangle, its perimeter is the sum of all for sides. We can write

Simplify

Solve for S

Example Question #63 : Quadrilaterals

Given a rectangle with a length  units longer than its width and an area of  square units, find the length of the rectangle's shortest side.

Possible Answers:

Correct answer:

Explanation:

The given rectangle has a length that is  units longer than its width. This can be expressed in the following equation, where  is the length and  is the width of the rectangle.

Since the area of the rectangle is equal to its length multiplied by its width (), and the area of the rectangle is given, the following equation must be true.

Replacing  in this equation with its value stated in the first equation results in the following.

Distribute the variable into the parentheses.

Factor the polynomial.

 and  are both solutions for this equation, but  is not valid as a width for a rectangle. The width of the rectangle is  units, which is the shorter side since the length is  units longer .

Example Question #1 : How To Find The Length Of The Side Of A Rectangle

There is a regtangular fence surrounding a park. The perimeter of the fence is . What is the width of the fence if the length is ?

Possible Answers:

 

 

 

 

 

Correct answer:

 

Explanation:

The formula for the perimeter of a rectangle is:

, where represents the length and represents the width.

We know the perimeter of the rectange is  and the length is . Plugging these values into the equation, we get:

 

  

Example Question #2 : How To Find The Length Of The Side Of A Rectangle

A rectangle has a perimiter of 36 inches and a length of 12 inches.  What is the width of the rectangle in inches?

Possible Answers:

Correct answer:

Explanation:

To find the width, multiply the length that you have been given by 2, and subtract the result from the perimeter. You now have the total length for the remaining 2 sides.  This number divided by 2 is the width. 

Example Question #1 : How To Find The Length Of The Side Of A Rectangle

A rectangle four and a half times as long as it is wide has perimeter of 272 centimeters. To the nearest tenth of a centimeter, how wide is it?

Possible Answers:

Correct answer:

Explanation:

If we call the width of this rectangle , then its length  can be restated as, or, equivalently, .

The perimeter can then be written as:

Since the perimeter of the rectangle is 272 cm, we can set up the following equation:

 

 

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