P 4 s P S S S 1 2 3 Perimeter and Circumference - PowerPoint PPT Presentation

D AY 133 – S PECIAL P RODUCTS

S TEPS TO S OLVING P OLYNOMIAL W ORD P ROBLEMS 1. Determine the geometric relationship. Write down the equation or formula needed to solve the problem. 2. If a diagram isn’t given, draw one of the shape or shapes and label the dimensions given. 3. Substitute values from the word problem into the formula. 4. Do the math to simplify or solve.

First do a quick review of perimeter and circumference relationships Perimeter and Circumference Triangle Square S 2 S 1 S S 3     P 4 s P S S S 1 2 3

Perimeter and Circumference Rectangle Circle (circumference) r w d l         P 2 l 2 w or P 2 ( l w ) C d or C 2 r

E XAMPLE 1 The sophomore class is working on a float for the homecoming parade. They need to put a fringe around the perimeter of a rectangular trailer. If the length is 6 feet longer than the width, what is the equation that represents how long the fridge needs to be.

E XAMPLE 1 Step 1: The geometric shape in the word problem is a rectangle, and you need to know the perimeter. Write down the formula.  2  P l 2 w

E XAMPLE 1 Step 2: Draw a diagram of the shape and label it with the given dimensions or information. In this example, you are given length in terms of width. Label width as w and length as w + 6 . w (width) w + 6 (length)

E XAMPLE 1 Step 3: Substitute the values from the diagram into the perimeter formula.    P 2 ( w 6 ) 2 w

E XAMPLE 1 Step 4: Use the distributive property to simplify the equation, and then combine like terms. That’s all you need because the problem only asked for the equation and not the solution.    P 2 w 12 2 w   P 4 w 12

E XAMPLE 2 The sophomore class is working on a float for the homecoming parade. They need to put a fringe around the perimeter of a rectangular trailer. The length is 6 feet longer than the width. If 52 feet of trim is used, what is the length and width of the trailer? This is the same problem as in Example 1, but this time, you are given enough information to solve for length and width.

E XAMPLE 2 Step 1: Write down the perimeter formula for a rectangle.  2  P l 2 w

E XAMPLE 2 Step 2: You can label a diagram as before, but this time you have one additional piece of information. The length of the trim represents the perimeter of the rectangle. You may want to add that to your diagram. P = 52 feet w (width) w + 6 (length)

E XAMPLE 2 Step 3: Substitute the values from the diagram into the perimeter formula.    52 2 ( w 6 ) 2 w

E XAMPLE 2 Step 4: Now solve for w, and you get w = 10 . Don’t forget the unit, which is feet.   52 4 w 12  10 w feet

E XAMPLE 2 Once you have width, you can also solve for length. Remember length is w + 6 . the Length must be 16 feet. You have now answered the question --- width is 10 feet, and length is 6 feet.   l w 6    l 10 6 16 feet

E XAMPLE 3 What expression represents the perimeter, P , of the triangle shown? 3  2 x 2  1 x  5 x Sometimes the diagram is already given.

E XAMPLE 3 Step 1: The geometric relationship is perimeter of a triangle, so write the equation for perimeter.    P S S S 1 2 3

E XAMPLE 3 Step 2: Substitute the values from the diagram into the perimeter formula.       P x 5 2 x 1 3 x 2

E XAMPLE 3 Step 3: Simplify by doing the addition and combining like terms. The expressions is simply 6x+4.  x 6  P 4

E XAMPLE 4 A circular driveway has an unknown radius of x feet. If the radius was increased by 5 feet, write an expression that would represent the new circumference.

E XAMPLE 4 Step 1: The geometric shape is a circle, and relationship is circumference. Write the formula.   C 2 r

E XAMPLE 4 Step 2: Draw a diagram and label it. The new radius is x + 5. r = x + 5

E XAMPLE 4 Step 3: Substitute the values from the diagram into the circumference formula.    C 2 ( x 5 )

E XAMPLE 4 Step 4: Use the distributive property to simplify the expression. In this type of problem, you are not solving for a value, so it is okay to leave the symbol for pi as it is.    2 x 10

A REA Triangle Square h s b 1 A  2  S A bh 2

A REA Rectangle Circle h r l   A  2 A r lw

A REA Trapezoid b 1 h b 2 1  1  A ( b b ) h 2 2

E XAMPLE 5 What is the expression that represents the area of the trapezoid shown?  x 2 x 3  x 8

E XAMPLE 5 Step 1: the geometric relationship is the area of a trapezoid. This is one you may not have memorized. If you can’t remember the formula, check the formula sheet. Write the formula for area of a trapezoid 1 1  ( b b ) h 2 2

E XAMPLE 5 Step 2: Substitute the values from the diagram into your equation. The bases are x + 2 and 3x + 8. The height is x. 1    ( 3 x 8 x 2 ) x 2

E XAMPLE 5 Step 3: Simplify by doing the math. First, add the binomials in the parenthesis 1  ( 4 x 10 ) x 2 Then multiply both terms by x. 1 x  2 ( 4 10 x ) 2 1 Finally multiply by The final expression is . 2 2  2 5 x x

Sometimes a figure is made up of more that one geometric shape. You may need to add or subtract one shape from another to get the area. E XAMPLE 6 A rectangular parking lot has a small rectangular area in one corner that needs to be repaired. The dimensions are shown in the drawing. What is the area of the parking lot that does NOT need repair? 2 x ft x ft 7 x ft 13 x ft

E XAMPLE 6 Step1: The geometric relationship is the area of a rectangle. A  lw

E XAMPLE 6 Step 2: In this problem, you have two rectangles. You need to express the area of both to find the answer. The mathematical relationship you need for the area NOT needing repair is the area of the large rectangle minus the area of the small rectangle Large Area Small Area -

E XAMPLE 6 Step 3: Substitute the values from the diagram into your equation.    13 x 7 x 2 x x

E XAMPLE 6 Step 4: Simplify by doing the math and combining like terms. The answer is 89x 2 x  2 2 91 2 x 2 89 x