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1:4

10/30 * 60/80 = 1/4

Spring door stop

Mmmm....this is an  interesting question

Let  the  base angles of  both triangles  be  equal

And let's assume that we  can create  similar triangles

Let  the  base  angle  in one triangle  = x and  the apex angle = y

Their sum is   x  +  y

Now   let  the  base  angle  of  another  triangle = (x - a)   and let  the apex angle = (y + a)   where  a is positive

Their sum  is also  x +  y

In the first   triangle    2x  +  y   =180

In the  second  triangle

2 ( x - a)  + ( y + a )    =180     simplify

2x  + y   - a   = 180

2x  + y  =  180 +  a

Since  a  is  positive....2x + y   in one  case  =180    and in the other case it is more  than 180

This is impossible.....so.....since  the  final result leads to an  absurdity.....our  assumption must  be false....

So....the  triangles cannot  be made similar    by   having  the  same  sums  for  one base angle and  the apex angle

I need help on this too.

 (sqrt(8)*sqrt(3)*2sqrt(5))/(4sqrt(6)*3sqrt(15))

Simplifying  we  have

sqrt (24) * 2sqrt (5)                     2 sqrt ( 24 * 5)              2 sqrt  (120)

_________________    =         ________________ =   __________   =   

4 sqrt (6)  * 3sqrt (15)                 12  sqrt ( 15 * 6)           12 sqrt  (90)

(2/ 12)  sqrt  (  120  / 90)    =

(1// 6)  sqrt (4/3)  =

(1/6)   sqrt (4)  / sqrt (3)   =

(1/6) * 2  / sqrt (3)  = 

(1/3)  /sqrt (3)  =

       1

_________                    rationalize  this  by  multiplying top/bottom by  sqrt  3    and we  get

  3sqrt (3)

sqrt  3

______

    9

Maybe  your worksheet  does  not  rationalize  the denominator  ????

You  certainly got  the  correct answer as I  would express it    !!!!

Like ya cut g

My feelings exactly, EP    !!!!!

Yikes !!!!!!!     

help asap!

A Golden Rectangle  is  one where  the  sides are in proportion  of  1  : Phi

Where Phi =  (1 + sqrt 5 ) / 2  ≈  1.618

Find   the area  of  the ltriangle

Semiperimeter, S =   (7 + 11 + 14)  /2  =  16

Area of  triangle=  sqrt  [16 8 (16 - 70 (16 - 11) (16 - 14) ]    =   sqrt [ 16 * 9 * 5 * 2 ]  =  12 sqrt (10)

We  can find  the   height of the  triangle  thusly

Area  = (1/2) AC *  height

12sqrt (10)  = 7 * height

(12/7) sqrt 10  =  height     ....call  this BD

Let the rectangle  be MNOP   where  AP  +  PO  +  OC  =   14

Let  the  height of  the  rectangle = a     and  let PO  =   a * Phi

We can  find   DC   as      sqrt  [ 11^2  - (12/7 * sqrt 10)^2 ]  = 67/7

And we  can  find  DA  as  sqrt [ 7^2  - (12/7 * sqrt 10)^2 ] =  31 / 7

By similar    triangles

OC  / a    =   DC / BD

OC  = a  *  ( 67/7)/ [ (12sqrt 10 / 7  ]    =   67 a /  [ 12 sqrt 10] 

AP   /  a  =  DA / BD

AP  =  31a  /[ 12sqrt 10 ]

So

AP  +  PO  +  OC    =14

31 a / [ 12sqrt10 ]  +  (1 + sqrt 5] / 2 * a  +  67a / [12sqrt 10 ]  =  14

Solving for  a  we get  that  a  ≈  3.3329

So  the  area of  the rectangle       a *  a * Phi  =    (3.3329)^2 * 1.618    ≈  17.97  units ^2

YOU are the one who can't answer the question......WHAT does that say about YOUR brains?        LOL !!!!  

Here is ONE way .....calculate the area of the red rectangle ...then subtract the 4 triangles

5 x4     -  2 * 1/2 (1 * 3) -  2 * 1/2 (4 * 1) =   20 - 3 - 4 = 13 units ²             as TA  posted !

Hey there, Guest!

The answer is 13 units squared.

You have to count and then do some division.

Hope this helped! :)

( ﾟдﾟ)つ Bye

The only solution is (x,y) = (-1,1), so the answer is (-1) + 1 = 0.

l^2 = 180.

Cool !    Thanx for the follow- up     ............   ~EP

3 is to x      as    (3+4.5)  is to x+6

3/x   =   7.5 / (x+6)

3x+18 = 7.5x

4.5 x = 18

x = 4      then CD = 4+6 = 10 units

Yep 360 was right 

If someone doesn't understand the Latex I might be able to translate it but if you can that wpuld be great

j = d       Given

(j - 36) * .5 = (d+36) * .75    sub in red equation fo j

(d-36) * .5 = .75 d + 27

.5 d - 18 = .75 d + 27

.25 d = -45      obviously there is a problem in the wording of the question

IF it said this instead:

When DON  gave JAKE $36, 50% of the amount of money Jake had left was the same as 75% of what Don had left.

THEN

(j+36) * 5 = (d-36) * .75

.5 d + 18 = .75d - 27

.25 d = 45

d = 180   dollars each to start    =    360 total dollars

tysm!!!
i know the answers but.. still

edit: forgot to mention that #4 and #5 is wrong :(
        i won't tell you the answer just in case someone else answers but....