Geometry Part 1B Perimeter By Julia Arnold, Dick Gill and Marcia Tharp for Elementary Algebra Math 03 online - PowerPoint PPT Presentation

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Geometry Part 1BPerimeterByJulia Arnold, Dick Gill and Marcia Tharpfor Elementary Algebra Math 03 online

Perimeter is the distance around an object.

If the object is arectangle, then it has 4 sides and opposite sides are equal in length and parallel to each other.The formula for its perimeter is

P = 2L + 2W where L is length and W is width of the rectangle.

If the object is acircle, we call the perimeter the circumference and ancient mathematicians found its formula to be .

In many perimeter problems involving rectangles, you may

be asked to find the dimensions. The dimensions of a rectangle

are the width by length. For example, picture frames are

categorized by their dimensions, such as 8 by 10, or 11 by 14.

The sum of the dimensions represents half of the perimeter.

The dimensions are only half the perimeter.

A picture frame that is an 8 by 10 would have a perimeter of

2(8 + 10) or 36 inches.What would be the perimeter of an

11 by 14 picture frame?

Answer: An 11 by 14 inch picture frame would have a

perimeter of 2(11+14) = 50 inches.

Example 1: Suppose we have a rectangle with a perimeter of 26 inches.We are told that the length is 10 more than twice the width.Can we find the dimensions of the rectangle?

Define the variables:

Let x = width, then 10 + 2x = length

The sum of width and length is half the perimeter, thus...

x + 10 + 2x = 26/2

3x + 10 = 13

3x = 3

x = 1 inch This is the width.

2x + 10 = 2(1) + 10 = 12 which is the length.

The dimensions are 1 by 12.

Example 2. The perimeter of a rectangular lot is 440 meters. If the length is 150 m. find the width.

Let x = width

2L + 2W = P

2(150) + 2x = 440

300 + 2x = 440

300 + 2x - 300 = 440 - 300

2x = 140

x = 70 m, the width

or L + W = P/2

150 + x = 220

x = 220 - 150= 70 m, the width

Example 3. The length of a rectangle is 10 more than twice the width. Find the length and the width if the perimeter is 56 inches.

Go ahead and guess now. Remember that 2L + 2W = P or

2(L+W) = P or L + W = P/2

Let x = the width

2x + 10 = the length

2L + 2W = P

2(2x + 10) + 2x = 56

4x + 20 + 2x = 56

6x + 20 - 20 = 56 - 20

6x = 36

x = 6 inches, the width

2x + 10 = 2(6) + 10 = 22 inches, the length

Or 2x + 10 + x = 56/2

3x + 10 = 28

3x = 18

x = 6 inches, the width

2(6)+10=22 inches, the length

Example 4. The perimeter of a triangle is 85 cm. If the middle side is 5 cm. larger than the smallest side and the large side is twice the

smallest side, find each side.

2L + 2W = P only works for rectangles. Perimeter is the distance

around the outside of the figure. For a triangle then, the perimeter

is the sum of the three sides.

Let x = the smallest side

x + 5 = the middle side

2x = the largest side

x + (x + 5) + 2x = 85

4x + 5 - 5 = 85 - 5

4x = 80

x = 20 cm, the shortest side

x + 5 = 25 cm, the middle side and 2x = 40 cm

How would you find the perimeter of this

architect’s home plan?

Example 5:

20’

10’

This shape consists of a rectangle with two

Overlapping circles. Can we find the perimeter

If we know the dimensions of the rectangle?

This shows the outside of the figure which

Is the perimeter that we must find. The perimeter

Is actually two lengths of the rectangle and two

Semi-circles.

20’

10’

We need the formula for the circumference of a circle which is C = 2 pi( r) Where r is the radius of the circle.

An alternate formula is C = pi d where d is the diameter of the circle. pi is the number which is approximated by 3.141592654

Since the two semicircles are the same size the two parts make one complete circle. Thus the perimeter is

P = 20 + 20 + (10) = 40 + 10

Which is approximately 71.4’

20’

10’

Is the Greek symbol for Pi

Other four sided figures which have opposite sides equal are:

parallelograms which have opposite sides parallel as well.

A rhombus which has four equal sides with opposite sides parallel

What is the difference between rectangles, squares, parallelograms and rhombuses?

A square is a rectangle which has 4 equal sides and every angle is a right angle.

Rectangle

Square

A rectangle is a parallelogram because opposite sides are equal in both and opposite sides are parallel in both.

The difference between the two is the rectangle has four right angles.

A parallelogram has no right angles.

A square is a rhombus, because all four sides are equal and opposite sides are parallel

A rhombus is also a parallelogram because opposite sides are equal and parallel.

A square has

four right angles.

A rhombus has no right angles.

If a figure is called a quadrilateral, then that means it

has four sides, but they could all be different measurements and they do not have to have opposite sides parallel.

Your Turn

Work out the problems on the next

slides to see if you understand this

concept.

1. The perimeter of a rectangular lot is 440 meters. If the length is 150 m. find the width.

Complete Solution
2. The perimeter of a triangle is 85 cm. If the middle side is 5 cm. larger than the smallest side and the large side is twice the smallest side, find each side. Complete Solution

3. A rectangular lot has a perimeter of 80 feet and length of 25 feet.

What is the width of the lot?

Complete Solution

4. Mr. Green wants to make a rectangular garden plot. He wants the length to be twice the width plus 3 feet. If the perimeter of the lot is 66 feet, what are the dimensions of the lot?

Complete Solution

5. Mr. Fixit wants to fence in a rectangular lot where one side will be the wall of his barn. He has 60 feet of fencing available. If the length is 4 feet less than twice the width. What are the dimensions of the lot?

Complete Solution

6. A quadrilateral has sides measuring 16.5 in. , 17.3 in. , 21.8 in., 29.2 in.

What is its perimeter?

7. An Equilateral triangle has a side measuring 1.28 cm. What is its perimeter?

8. An Isosceles triangle has its equal side measuring 15.4 in. and its 3rd side measuring 23.9 in. What is its perimeter?

9. A square measures 1.63 m. What is its perimeter?

10. A rhombus measures 8.06 ft. on a side. What is its perimeter?

11. A parallelogram measures 47.2 on one side and 36.8 on another. What is its perimeter?

12. A rectangle has dimensions 57.9 by 39.8 in. What is its perimeter?

When complete go to next slide.

Complete Solutions

13. Find the circumference of the circle whose radius is 14.3 cm.

Round to the nearest tenth.

14. Find the circumference of the circle whose diameter is 8.4 in.

Round to the nearest tenth.

Find the perimeters of the indicated figures:

15.

6 ft.

17.

7 ft.

12 ft.

28 cm.

11 ft.

12 cm.

18 ft.

60.8 ft.

14 cm.

16.

46.0 ft.

16 cm

Complete Solutions

12 cm

Find the perimeter of this figure.

18.

15.3 cm.

19.6 cm

Complete Solutions

1. The perimeter of a rectangular lot is 440 meters. If the length is 150 m. find the width.

Length + width = 1/2 perimeter

150 + x = 440/2

150 + x = 220

x = 70

The width is 70

Return to Problems

2. The perimeter of a triangle is 85 cm. If the middle side is 5 cm. larger than the smallest side and the large side is twice the smallest side, find each side.

X = smallest side

x + 5 = middle side

2x = largest side

x + x + 5 + 2x = 85

4x + 5 = 85

4x = 80

x = 20

X = 20

x + 5 = 25

2x = 40

check

20 + 25 + 40 = 85

Let x = width

x + 25 = 80/2

x + 25 = 40

x = 15 The width of the lot is 15 feet.

4. Mr. Green wants to make a rectangular garden plot. He wants the length to be twice the width plus 3 feet. If the perimeter of the lot is 66 feet, what are the dimensions of the lot?

Return to Problems

Let x = width, length = 2x + 3

x + 2x + 3 = 66/2

3x + 3 = 33

3x = 30

x = 10 2x + 3 = 23 The dimensions are 10 x 23 feet.