A boy and a girl playing with pencil. The girl break the pencil
in two parts and the boy observe that the ratio of lenglh of
these two parts is same as the valio of length of pencil
to the larger part. Find the ratio in which Ih@giul break the pencil
Answers
- Required ratio of smaller part to the larger part is equal to (√5 - 1) : 2 .
- Required ratio of larger part to the smaller part is equal to (√5 + 1) : 2 .
Given :-
- The ratio of length of these two parts is same as the ratio of whole pencil to the larger part .
To Find :- Ratio in which the girl break the pencil ?
Solution :-
- Let smaller part of pencil length = S unit
- Larger part of pencil length = L unit
- Original length of pencil = (S + L) unit
Now, it is given that, the ratio of smaller part of the pencil to the larger part is equal to larger part to the original length of the pencil .
So,
→ S : L = L : (S + L)
→ S/L = L/(S + L)
→ L² = S² + LS
→ S² + LS - L² = 0
Solving for S by using Sridharacharya formula we get :-
- a = 1
- b = L
- c = (-L²)
So,
→ S = {(-b) ± √(b² - 4ac)}/2a
→ S = (-L ± √(L² + 4L²)/2
→ S = (-L ± √5L²)/2
→ S = (-L ± L√5)/2
→ S = L(-1 + √5)/2
→ S/L = (√5 - 1)/2
→ S : L = (√5 - 1) : 2 (Ans.)
Also, if asked L : S then :-
→ L : S = 2 : (√5 - 1)
→ L/S = 2/(√5 - 1)
→ L/S = {2/(√5 -1)} × {(√5 + 1)/(√5 + 1)}
→ L/S = 2(√5 + 1)/(5 - 1)
→ L/S = 2(√5 + 1)/4
→ L/S = (√5 + 1)/2
→ L : S = (√5 + 1) : 2 (Ans.)
Learn more :-
A hundred people participated in a flash mob. First, they formed a circle. MJ marked as number one had a torch. He point...
https://brainly.in/question/38163805
HELP-ASAP-A single line of four cats one behind the other walks towards and head-on into a single line of five cats walk...
https://brainly.in/question/38409325