+0  
 
+1
207
5
avatar+1307 

Also this:

 

Next, 

 

And finally,

 Jun 29, 2018
edited by AWESOMEEE  Jun 29, 2018
 #1
avatar+98196 
+2

Here's the second one

 

MIR  is an inscribed angle

 

So....since it subtends minor arc  MR, the  angular measure of this arc  is twice 18° = 36°

 

So......the length  of MR  is given by :

 

2 pi  *  radius *  (36 / 360)  =

 

2pi * 80  * (1  /10) =

 

(160 / 10) pi  =

 

16 pi   cm

 

 

cool cool cool

 Jun 30, 2018
edited by CPhill  Jun 30, 2018
edited by CPhill  Jun 30, 2018
 #2
avatar+1307 
+1

Doesn't seem to work. I entered in 3.6pi, then 18pi/5.

 

I can't enter anymore, but I am still curious for the solution.

AWESOMEEE  Jun 30, 2018
edited by AWESOMEEE  Jun 30, 2018
 #3
avatar+98196 
+1

Sorry, AWESOMEEE...I had the wrong value for the radius...see the corrected answer...!!!

 

 

cool cool cool

CPhill  Jun 30, 2018
 #4
avatar+98196 
+2

Here's the first one....there might be an easier way to do it, however  !!!

 

The area of  ABC  is   (1/2) (16)^2 (√3/2)  =  64√3  cm

 

So...the area  of  equilateral triangle   PQR is   (1/4)  of this  = 16√3 cm^2

 

And we can find the   length of  PR  by using the area formula for PQR

 

(1/2) (PR)^2 (√3 /2 )  =  16√3 

 

(1/2) PR^2 (1/2)  = 16

 

PR^2  / 4  = 16

 

PR^2  = 64

 

PR  = 8  cm

 

And note that we have trapezoid BPRC  which has the same area as the small equilateral triangle

 

So   area  of trapezoid  BPRC  = area of triangle PQR

 also

(1/2) (height) ( sum of the bases)  = 16√3

 

height ( 16 + 8)  = 32√3

 

height (24)  = 32√3

 

height  =  32√3 / 24   =   (4/3)√3  cm

 

So...note  that if we draw a perpendicular  from P  to BC  this  will be the height of the trapezoid and will  also form one leg of a right triangle  with BP  as the hypotenuse

 

And the other leg length will be  ( BC  - PR)  / 2   = (16 - 8) /2  =  8/2  = 4

 

So....using the Pythagorean Theorem...we can find  BP  as

 

BP  =   √ [ 4^2  +  [ 4/3 * √3 ]^2  ]  =  √ [ 16  +  16/3  ]  =   4 √ [ 1 + 1/3] = 

 

4 √ [ 4/3 ]  = 8√ [ 1/3 ]  =  8 / √3  cm   =  8√3 / 3  cm

 

 

cool cool cool

 Jun 30, 2018
 #5
avatar+98196 
+2

Here's the third one

 

Orient the paper so that 22 is the width and 39 is the height

 

Note that  the number of retangles of (2 * 3)  that can  be cut from this sheet is

 

(39/3)  * ( 22/2)  = 

 

13  * 11  =

 

143

 

But each of the rectangles  can  be divided into two triangles with bases of 2 and heights of 3

 

So....the total number of triangles  is  143 * 2  =  286

 

 

cool cool cool

 Jun 30, 2018

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