+0  
 
+1
45
5
avatar+1311 

Also this:

 

Next, 

 

And finally,

AWESOMEEE  Jun 29, 2018
edited by AWESOMEEE  Jun 29, 2018
 #1
avatar+87293 
+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

CPhill  Jun 30, 2018
edited by CPhill  Jun 30, 2018
edited by CPhill  Jun 30, 2018
 #2
avatar+1311 
+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+87293 
+1

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

 

 

cool cool cool

CPhill  Jun 30, 2018
 #4
avatar+87293 
+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

CPhill  Jun 30, 2018
 #5
avatar+87293 
+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

CPhill  Jun 30, 2018

13 Online Users

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.