CPhill

2. A 3 meter wide sidewalk surrounds a rectangular garden that is 4 meters by 6 meters. Find the area of the sidewalk only.

If you can picture this......

We  have  four   3 x 3 squares at the corners =  4 * (3 * 3)   =  36 m^2

Also  we  have  two  4 x 3  rectangles on two sides  =  2 * ( 4 * 3)   =  24 m^2

And we  have two  6 x 3  rectangles on two sides  =  2 * ( 6 * 3)  = 36 m^2

Total area of sidewalk  =  (36 + 24 + 36)   =   96 m^2

First  one

Note  that  AB / DE  =  22 / 11  =  2 / 1  =  2

So  each correseponding side of ABC to that of DEF  is  twice as long

So

x  = 34 /  2   =  17

And 

y  =  2 * 13   =   26 

Number  on  any particular  square =  2^(n - 1)

On the  31st  square  we  have   2^(31 - 1) = 2^30  =  1073741824 grains

Total  cumulative  number  through  square  n  =  2^n  - 1 =  2^31 - 1  =  2147483647 grains

Total weight  =  2147483647 /  7000   ≈  306783 lbs

4.The ratio of similar triangles △ACB to △DFE is 2/5 and  AB = 8.  What is the length of DE? 

DE / AB =  5/2

So

DE  =  (5/2)AB

DE  = (5/2) * 8   =   20

5. △ACB is similar to △DFE.  The m ∠ABC = 35 and the m∠ACB = 80. What is the measure of ∠FDE?

FDE  =  CAB   =  180 - mABC -m ACB =    180  - 35  - 80  =  180  - 115   =  65°

2. A triangle with sides 8m, 11m and an included angle of 45°.  

How many triangles can be produced: _______

Explain:

One triangle.....we  have a SAS  situation.......the triangle  is well-defined

3. A triangle with angles 

25°, 56°, and 99°

How many triangles can be produced: _______

Explain:

An infinite  number  of similar triangles could  be  produced

1. Three segments have a total length of 26 inches. The first segment is two less than three times the second segment. The third segment is one more than five times the second segment. What are the lengths of the three segments? 

All three variables must be defined in terms of x.

(3x - 2)  +  x  +  ( 5x + 1)  =  26

9x - 1  = 26

9x  =  26 + 1

9x  =  27

x = 27 / 9  =  3

First segment  =   3(3) - 2   =   7  in

Second segment =  3  in

Third segment  =  5(3) + 1   =  16 in

Leg  of right triangle  =  L

Using the Pythagorean Theorem

2^2  = 2L^2

4 = 2L^2

2 = L^2

sqrt (2)  =  L

Area of right  triangle =   L^2  / 2   =   (sqrt 2)^2   2  =  2  / 2    =  1

Total area    1  + (1 * 2)  =   3

Area of triangle  / Area of Pentagon  =   1 / 3  =  33%

First one  

Total paid = 4 (7.05)  =   28.20

This  is  the  same  price   as  3 paid tickets and a  free one

So.....the  normal price would  be    28.20  / 3  =  9.40

Second  one

a   -17   - 13

b   25 - (-37)

c   you  should be able to do this one

a      31     50

b      Working backwards

           3rd   term =  33  - 19   =   14

           2nd term =    19  - 14   =   5

           1st term  =  14  -  5   =  9  

c   

1st term  =  n -  m

4th term =  m + n

5th term  =   n + ( m + n)  =   m + 2n