+0  
 
0
167
4
avatar+154 

A circle with radius r, is inside an equilateral triangle, with sides x cm 

The circumference of the circle touches each side of the triangle 

The area of the circle is 100 cm^2

Work out the value of x 

Give your answer to 2 significant figures

YEEEEEET  Feb 22, 2018
Sort: 

4+0 Answers

 #1
avatar+12266 
+1

First find the radius of the circle   area = pi r^2   r = 5.64 cm

Then   tan 30 = 1/2 / (sqrt(3) /2)) = r/(1/2x)   where x is side length

1/2 / sqrt 3/ 2 =  r/(1/2 x)

1/2 x  * .57735 = r   = 5.64    x = 19.53 ~~~ 20 cm (two sig-figs  

 See diagram below:

Ooops ...forgot diagram (and I found an error...fixed)

ElectricPavlov  Feb 22, 2018
edited by ElectricPavlov  Feb 22, 2018
edited by ElectricPavlov  Feb 22, 2018
 #2
avatar+86613 
+1

 

The radius of the circle  is :     sqrt [ (100) / pi ]  =  10 / sqrt (pi)

 

We can find 1/2 of the length of the side of the triangle thusly :

 

[ (1/2)x ] /  sin (60)  =  [10/ sqrt (pi)]  / sin (30)

 

x / [ 2 sqrt (3) /2 ]  =  2 * 10 / sqrt(pi)

 

 x / sqrt (3)   =  20/ sqrt(pi)

 

x =  20 sqrt (3)  / sqrt (pi)   =   20  sqrt (3/pi) ≈ 19.54 cm

 

( 20 cm  rounded to 2 sig figs )

 

 

 

cool cool cool

CPhill  Feb 22, 2018
 #3
avatar+12266 
+1

Here is the diagram I sketched:

ElectricPavlov  Feb 22, 2018
 #4
avatar+4 
+1

The radius of the circle  is :     sqrt [ (100) / pi ]  =  10 / sqrt (pi)

 

We can find 1/2 of the length of the side of the triangle thusly :

 

[ (1/2)x ] /  sin (60)  =  [10/ sqrt (pi)]  / sin (30)

 

x / [ 2 sqrt (3) /2 ]  =  2 * 10 / sqrt(pi)

 

 x / sqrt (3)   =  20/ sqrt(pi)

 

x =  20 sqrt (3)  / sqrt (pi)   =   20  sqrt (3/pi) ≈ 19.54 cm

ruozhoumath  Feb 23, 2018

30 Online Users

avatar
avatar
avatar
avatar
avatar
New Privacy Policy (May 2018)
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  Privacy Policy