New Batches at TathaGat Delhi & Noida!               Directions to CP centre
Geometry Problems....plz solve these
by Nakul Kothari - Thursday, 30 July 2009, 12:47 AM
  hi friends ....i am new to this site , infact this is going to be my first post....
here are some questions which i am not able to solve even after scratching my hairs for long....

Q 1. A piece of paper is in the shape of a right angled triangle. This paper is cut along a line that is parallel to the hypotenuse,leaving a smaller triangle.The cut was done in such a manner that there was a 35% reduction in the length of the hypotenuse of the triangle.If the area of the original triangle was 54 sq. inches before the cut what is the area of smaller triangle?

Q 2. What is the number of distinct triangles with integral valued sides and perimeter as 12?

Q 3. Consider two different cloth cutting processes.In the first one ,n square cloth pieces of the same size are cut from a square cloth piece of size a ; then a  circle of maximum possible area is cut from a square of the same size and the process ends there. The cloth pieces remaining after cutting are scrapped in both the processes . The ratio of  the total area of scrap cloth generated in the former to that in the latter is..?

Q 4. If a,b and c are the sides of a triangle and a2 + b2 + c2=bc + ca + ab , then the type of triangle is..?

Q 5. A cube of side 12 cm. is painted red on all the faces and then cut into smaller cubes each of side 3 cm. What is the total number of smaller cubes having none of their faces painted?

Q 6. A square whose side is 2 meters has its corners cut away so as to form an octagon with all sides equal. Then length of each side of the octagon in meters is..?

Please post the answers along with the detailed solutions....
Re: Geometry Problems....plz solve these
by kuldeep patel - Thursday, 30 July 2009, 12:11 PM
  1) area of smaller triangle 54*(65/100)^2
2) a+b+c =12
    total no od triangle =3
sides:
    2 5 5
    3 5 4
    4 4 4
3) first process is not clear
5) 8
6) 2- (2)^1/2
Re: Geometry Problems....plz solve these
by ujjawal kumar - Thursday, 30 July 2009, 01:21 PM
 

1)area of smaller triangle 8.45
2) a+b+c =12
    total no od triangle =3
sides:
    2 5 5
    3 5 4
    4 4 4
4)equilateral traingle

5) 8
6) 2- (2)^1/2

@ kuldeep patel
by Nakul Kothari - Friday, 31 July 2009, 12:37 AM
  Thanks for the answers....
As far as Q 3 is concerned it is:-
I Process:- n square cloth piece of the same size are cut from a square cloth piece of size a; then a circle of max. possible area is cut from each of the smaller squares.

II Process:- only one circle of max. possible area is cut from  a square of same size and the process ends

The cloth pieces remaining after cutting the circles are scrapped in both the processes. The ratio of total area of scrap cloth generated in the former to the latter is......?


  I couldn't understand the concept behind Q 6 and Q 4....can you please explain them in detail......
@ ujjawal kumar
by Nakul Kothari - Friday, 31 July 2009, 12:40 AM
  Thanks for the answers......
I couldn't understand the concept behind Q 6 and Q 4....can you please explain them in detail......
Is there any concept behind Q 2 (guessing the sides of a triangle) or is it just hit and trial method....
Re: @ ujjawal kumar
by kuldeep patel - Friday, 31 July 2009, 07:01 AM
  Q 4. If a,b and c are the sides of a triangle and a2 + b2 + c2=bc + ca + ab , then the type of triangle is..?

put a=b=c
that is the method...
Re: Geometry Problems....plz solve these
by userdce . - Friday, 31 July 2009, 10:57 AM
 

6) let AC=l=CD so

AC^2=AB^2+BC^2 BC and AB are equal due to symmetry

 l^2=2[(2-l)/2]^2 so calculate l ans so is answer

2(sqrt(2)-1)


Re: Geometry Problems....plz solve these
by Nakul Kothari - Friday, 31 July 2009, 11:38 PM
  Thanks for the approach

Here are two more questions which are troubling me :-
Q 1-The area of the circle circumscribing three circles of unit radius touching each other is...?

Q 2-Circles are drawn with four vertices as the center and radius equal to the side of the square.If the square is formed by joining the midpoints of another square of side 2(6^0.5),find the area common to all the four circles...?
Re: Geometry Problems....plz solve these
by Sarvesh Kumar - Saturday, 1 August 2009, 07:23 PM
 

Q 1-The area of the circle circumscribing three circles of unit radius touching each other is...?

Ans:    pi*(2+sqrt(3))^2/3



Q 2-Circles are drawn with four vertices as the center and radius equal to the side of the square.If the square is formed by joining the midpoints of another square of side 2(6^0.5),find the area common to all the four circles...?

 

Ans:    4*pi - 12(sqrt(30)-1)

Re: Geometry Problems....plz solve these
by Sarvesh Kumar - Saturday, 1 August 2009, 10:29 PM
 

Sorry there was a typo in earlier post. Actually I meant   4*pi - 12(sqrt(3)-1)   as a answer for Q 2...smile 

Re: Geometry Problems....plz solve these
by Nakul Kothari - Saturday, 1 August 2009, 11:21 PM
  thanks sarvesh.....but please could you explain your solution.....i can't even start the solution!!!!
Re: Geometry Problems....plz solve these
by userdce . - Sunday, 2 August 2009, 01:04 PM
 
from the figure

angle A=60=angle B
calculate AC...
then AC would come to be 2/sqrt(3) and radius of larger circle would be
1+2/sqrt(3)
so area can be calculated

it would come to be whatever Sarvesh has calculated
just try NAKUL and let us know if u get it

Re: Geometry Problems....plz solve these
by userdce . - Sunday, 2 August 2009, 01:14 PM
  NAKUL
try to give answers also friend

Re: Geometry Problems....plz solve these
by Nakul Kothari - Monday, 3 August 2009, 12:23 AM
  thanks userdce.......
from my next post I will surely post the available answers...

The answers are :-
1) (pie/3)(2+(3)^1/2)2

2) 4 pie -12 (3^.5  -1)
Re: Geometry Problems....plz solve these
by neha singhal - Monday, 23 March 2015, 01:41 AM
  very good appproach