Types of word problems: 

1) Dimensions of a rectangle given the area

2) Flight of an object

3) Shaded region of a shape

 

 

 

Example 1: Dimensions of a rectangle given the area

 

a) Determine the binomials that represent the dimensions of the rectangular garden

The area is given in standard form x2+8x+15           5 x 3 = 15

WE NEED TO FACTOR!                                                   5 + 3 = 8                  

 

= (x+5)(x+3)

      l    x  w

 

b) Determine the dimensions if x represents 2 m

  l = x+5                  w= x+3

  l = 2+5                  w= 2+3

  l = 7                       w = 5                       Therefore, the dimensions are 3m x 4m 

 

 

 

 

 

Example 2: Flight of an object

 

The height of the ball thrown from the top of a building can be measured by the formula h= -5t^2+20t+60, where t is the time in seconds and h is the height in metres.

 

a) Write the formula in factored form

= -5(t-6)(t+2)                               -6 x 2 = -12

                                                     -6 + 2 = -4

 

 

b) When does the ball land on the ground? [ Zeros]

h = -5(t-6)(t+2)= 0

t-6=0         t+2=0                      Therefore, the ball lands at 6 seconds.

t= 6             t= -2

 

c) What is the maximum height the ball will reach and when does it reach its maximum height? [Vertex (2,80)]

 

AOS: 6+(-2)                                                               h= -5t^2+20t+60   

             2                                                                   h= -5(2)^2+20(2)+60              Therefore, the maximum height of the ball is 80m 

= 2 [Sub into orginial equation]                             h= -5(4)+40+60                         and the ball lands at 2 seconds to it maximum height.

                                                                                  h= -20+40+60         

                                                                                  h=80

 

 

 Example 3: Shaded region of a shape                

 

a) Write the area expression in factored form to represent the shaded region[Expand]  

 

Big Square:                                           Small Square:

 

=(3x+4)^2                                              =  (x-6)^2  

=(3x+4)(3x+4)                                       =   (x-6)(x-6)

= 9x2+12x+12x+16                              = x2-6x-6x+36

=9x2+24x+16                                        = x2-12x+36

 

 

[Hint: Big Square - Small Square = Shaded Area ]

 

* Use the standed form equations *

 

=9x2+24x+16 - (x2-12x+36) [Put brackets on the second bracket since it is being subtracted]

= 9x2+24x+16 - x2+12x-36 

= 9x2-x2+24x+12x+16-36 [Collect like terms]

= 8x2+36x-20  

 

Therefore the area of the shaded region is 8x2+36x-20 

 

 

b) If x=5. find the area of the shaded region                 

 

[Sub x=5 into equation 8x2+36x-20] 

 

= 8(5)^2+36(5)-20

= 8(25)+ 36(5)-20

= 200+180-20

= 360

 

Therefore, the area of the shaded region is 360 cm2

 

 

 

FACTORED FORM EXIT TICKET[ Optional]