Word Problem #1

 

1.Write and simplify an expression to repersent the area of the given composite figure.

 

 

 

 

 

 

 

 

 

 

 

 

Step 1:Make an expression

(x+4)(x-4)+(2)(x)

 

Step 2:Expand and simplify

(x+4)(x-4)+(2)(x)

 

 

 

 

 

 

 

 

 

 

 

 

 

Final answer: (x2-16)+(2x)

 

 

Word Problem #2:

 

2.A rectangle has a primeter of 20m and an area of 10m2. Determine the dimentions of the rectangle.

 

Step 1: Draw a rectangle

 

 

 

 

 

 

 

 

 

 

 

 

 

Step 2:Do perimeter formula p=2L+2W 

 

p=2L+2W

 

20=2L+2W

-2L-2L

 

20-2L=2W

   2         2

 

20-2L=W

   2

 

10-1L=W        

 

 

Step 3: Now that you have find your width formula fit that in the area formula to find your length

 

A=LXW

 

10=LXW

 

10=L(10-L)

 

10=10L-L2

-L2       -L2

 

L2-10=10L

-10L   -10L

 

L2-10L-10=0

 

Step 4: Now that you got it into standered form put it into quadratic form to find your length. 

 

L2-10L-10=0

A- 1

B- -10

C- -10

x=-b+-√ b2-4ac  

           2a

x=-(-10)+-√ 102-4(1)(-10)  

                 2(1)

x=10+-√ 100+40  

                 2

x=10+-√ 140  

            2

x=10+-11.8 

            2

x=10+11.8            x=10-11.8

           2                         2

x=21.8                    X=-1.8

         2                           2

X=10.9                   X=-0.9    

 

Step 5:Put in both answers into width formula.

10-1L=W                  

10-1(10.9)=W        10-1(-0.9)=W                  

10-10.9=W             10+0.9=W          

-0.9=W                   10.9=W

 

Step 6:The smaller number you get for your witdh is the answer because width is smaller then length.

 

Therefore the lenght is 10.9m and width is -0.9m