Triangle

For ten years a teacher exposed his student to the following test:

A right-angle triangle has hypoteneuse 10 inches, and the height drawn from the right angle to the hypoteneuse is 6 inches. Find the area of this right-angle triangle.

For 10 years the students satisfied their teacher with the following answer: Area = (10*6)/2 = 30 square inches.

Then at the eleventh year a smart student came, who could not solve this problem. Why?

Solution

 Data (i.e. the things given):  Angle at A a right angle, AP perpendicular to BC, BC = 10,  AP = 6.

Quaesita (the things sought):  Area of the triangle ABC.

Naive approach (wrong):  Area of a triangle is half the base times the height.  In this case the base is 10, the height is 6, so the area is 30 square units.

Smart approach (correct):  Construct a circle with BC as diameter.  Plainly the radius of this circle is 5. 

By a well-known theorem of plane geometry (Euclid’s III.31), if the angle at A is to be a right angle, then A must lie on the perimeter of the circle. 

It follows that the maximum possible value of AP is 5.

The triangle as given is therefore an impossible object, and the problem has no solution.

The Monkey’s Mother

 

A rope hangs over a pulley.  On one end is a weight.  Balanced on the other end is a monkey of equal weight.  The rope weighs 4oz. per foot.  The age of the monkey and the age of its mother together equal 4 years.  The weight of the monkey is as many pounds as its mother is years old.  The mother is twice as old as the monkey was when the mother was half as old as the monkey will be when the monkey is three times as old as the mother was when the mother was three times as old as the monkey.  The weight of the weight plus the weight of the rope is half as much again as the difference between twice the weight of the weight and the weight of the monkey.  How long is the rope?

General Knowledge No.31

1) Rubina Ali, nine-year odl child artist who played in the movie ‘Slumdog Millionaire’ will publish her autobiography next month. What will it be named?

2) Housing ministry has launched a new scheme, with an initial budget of Rs.5,000 crore. It aims to construct 10 lakh affordable hourses, setting an ambitious target of making India slum-free in five years. Name the scheme.

3) Which Indian university conferred with a honarary doctrate to Oscar winning music director A.R. Rehman?

4) Recently an Indian nuclear scientist Mr.Lokanath Mahalingam went missing from an nuclear power plant and few days later his body was found in Kali river. Name the power plant?

5) He holds record for maximum number of centuries in Twenty 20 Cricket(Domestic+International). Identify this player

.

.

.

The answers are:

1) Slumgirl Dreaming: My Journey to the Stars

2) Rajiv Gandhi Aawas Yojana

3) Aligarah Muslim University

4) Kaiga Nuclear Power Plant (Karnataka)

5) Ian Harvey

Puzzle No.32

A trout’s tail weighs eight pounds. Its head weighs as much as the tail and one-half of the body combined, and the body weighs as much as the head and tail combined. What does the whole trout weigh?

.

.

.

The answer is: 64 pounds

We have t = 8;     h = 8 + b/2;     b = h + 8.

Then, h = 8 + (h + 8)/2 –> h = 24, and b = 32; therefore, the whole trout weighs 64 pounds.

Puzzle No. 31

What is the smallest prime number with 3 distinct digits that remains prime no matter which one of its digits is removed?

.

.

.

The answer is:

137

General Knowledge No.30

1) The iconic $31-billion Scandanavin home products giant, has put on hold its plans to set up 25

showrooms across the country(India) for an investment of around $1 billion, due to India’s rules on FWI in retail say the foreign company can’t hold more than 51% stake and must have an Indian

partener. Name the company?

2) India’s second largest CDMA telecom company Tata Teleservices announced the launch of services

in GSM platform in partnership wih Japanese telecom service provider NTT DoCoMo. What will the service be branded as?

3) He drew inspiration from his elder brother Rajaram, a former National Junior Champion, and was inducted into the sport by Earnet Lakhra. In his first internation meet, this 16-year old fly-weight boxer has won Bronze medal at World Junior Boxing Championship in Armenia, this year. Who is Indian boxer?

4) This year English county side ‘X’ signed 20-year old Indian leg-spinner ‘Y’ on a short-term contract, interestingly ‘Y’ scored a century in his very first appearence for ‘X’. Identify ‘X’ and ‘Y’

5) Identify the company from logo

The answers are:

1) IKEA (Ingvar Kamprad Elmtaryd Agunnaryd)

2) Tata-DoCoMo

3) Namit Bahadur

4) X= Sussex, Y=Piyush Chawala

5) Arcelor Mittal

General Knowledge No.29

1) In recently held World T20 World Cup top two run scorers were TM Dilshan (Sri Lanka) and Jaques Kallis (SA) scoring 317 and 238 respectively. Who were the top two run getters in the first edition of T20 World Cup in 2007?

2) Most of you would have voted during recently held Lok Sabha polls, an indelible ink is used to mark your finger. This ink stains the skin on contact with sun light. Can you name the chemical which attributes to this stains as a result of which the mark stays for at least two weeks.

3) Britain’s Royal Mail issued a set of stamps on February 12, 2009 to mark the 200th anniversary of which scientist?

4) State owned domestic airline of India, ‘Indian Airlines’ has been renamed as ‘Indian’. What is the new logo of ‘Indian’ and from where it has been taken?

5) Identify these two leaders in the picture, who were in news recently

The answers are:

1) Matthew Hayden (Aus) & Gautam Gambhir (Ind)

2) Silver Nitrate

3) Charles Darwin

4) Logo: Chakra, Source: Sun temple, Konark (Orissa)

5) Ayatollah Ali Khamenei and Mohammad Ahmedinejad (Iran)

Puzzle No.30

A man is trapped in a room. The room has only two possible exits: two doors. Through the first door there is a room constructed from magnifying glass. The blazing hot sun instantly fries anything or anyone that enters. Through the second door there is a fire-breathing dragon. How does the man escape?

Answer:

He wait for the sun to set and get out during night.

General Knowledge No.28

1) According to George W Bush, which three countries formed the Axis of Evil?

2) DR Mahathir Mohamad, the longest serving asian Head of Government, retired in 2003. He was Prime Minister of which country?

3) Who was the last President of USSR?

4) George Bush and Tony Blair were famous for their closeness. To which pairs have they been compared?

5) Identify this lady in the picture, should be an easy one as clue is in the picture…

The answers are:

1) Iran, Iraq and North Korea

2) Malaysia

3) Mikhael Gorbachev

4) Ronald Reagan and Margaret Thatcher

5) Margaret Thatcher

Puzzle No.29

My brother, Julian, is a little simple. I recently asked him to buy me some ribbon for my daughter’s pretty pink bonnet. He went to the haberdashery shop for the required length but accidentally interchanged the feet and inches. When I measured the resulting ribbon I only had 5/8 of the length I required. How much ribbon did I originally ask for?

Answer:

I asked for 7 feet, 4 inches and my brother brought me 4 feet, 7 inches. If we label what I asked for as A feet and B inches, which is (12 x A + B) inches, then I actually received B feet and A inches, which is (12 x B + A) inches. Which means that:

(5 / 8 ) x (12 x A + B) = (12 x B + A)

Simplifying gives:

A = (91 / 52) x B

As B is the number of inches, it can only be between 1 and 12 and must give A as a whole number of feet. B = 4 is the only possible value, which means that A = 7. So I originally asked for 7 feet, 4 inches.