Solve the following mathematical problems:

A circle is inscribed inside a right angled triangle with equal sides. What is the area of the circle if the length of one side of the right angled triangle is 4cm?

Created: 3 months ago | Updated: 2 months ago

Job Solution Sonali Bank Ltd Sonali Bank Ltd. || Senior Officer (29-06-2018) || 2018 গণিত

প্রশ্নে বলা হচ্ছে যে, একটি সমকোণী সমদ্বিবাহু ত্রিভুজে একটি বৃত্ত অন্তর্লিখিত আছে। ত্রিভুজটির একবাহুর দৈর্ঘ্য (সমান সমান বাহুর একটি) 4cm হলে বৃত্তটির ক্ষেত্রফল কত?

Depict the following figure according to question

Area of ABC triangle $= \frac{1}{2} \times b a s e \times h e i g h t$

$= \frac{1}{2} \times 4 \times 4 = 8 c m^{2}$

Now, $A C^{2} = {(A B)}^{2} + {(B C)}^{2} = 4^{2} + 4^{2} = 16 + 16 = 32$

$∴ A C = \sqrt{32}$

The radius of a circle inscribed in a triangle $= \frac{2 \times A r e a o f t r i a n g l e}{P e r i m e t e r o f t r i a n g l e} = \frac{2 \times 8}{(4 + 4) + \sqrt{32}} = \frac{16}{8 + (\sqrt{2 \times 4^{2}})}$

$= \frac{16}{8 + 4 \sqrt{2}} = \frac{16}{4 (2 + \sqrt{2})} = \frac{4}{2 + \sqrt{2}} = \frac{2 \times \sqrt{2} \times \sqrt{2}}{\sqrt{2} (\sqrt{2} + 1)} = \frac{2 \sqrt{2}}{\sqrt{2} + 1} = \frac{2 \sqrt{2} (\sqrt{2} - 1)}{(\sqrt{2} + 1) (\sqrt{2} - 1)} = \frac{2 \sqrt{2} (\sqrt{2} - 1)}{2 - 1} = 2 \sqrt{2} (\sqrt{2} - 1) ∴ R a d i u s = 2 \sqrt{2} (\sqrt{2} - 1) c m ∴ A r e a o f c i r c l e = {πR}^{2} = π {\{2 \sqrt{2} (\sqrt{2} - 1)\}}^{2} = π 4 \times 2 {(\sqrt{2} - 1)}^{2} {cm}^{2} = 8 π 2 \sqrt{2} {(\sqrt{2} - 1)}^{2} {cm}^{2} (ans .)$

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A teacher has 3 hours to grade all the papers submitted by the 35 students in her class. She gets through the first 5 papers in 30 minutes. How much faster does she have to work to grade the remaining papers in the allotted time?

Created: 3 months ago | Updated: 2 months ago

Job Solution Sonali Bank Ltd Sonali Bank Ltd. || Senior Officer (29-06-2018) || 2018 গণিত

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Solve the following mathematical problems:

A two digit number is four times the sum of the two digits. If the digits are reversed, the number so obtained is 18 more than the original number. What is the original number?

Created: 3 months ago | Updated: 2 months ago

Job Solution Sonali Bank Ltd Sonali Bank Ltd. || Senior Officer (29-06-2018) || 2018 গণিত

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Solve the following mathematical problems:

Solve: $x^{2} - x y = 7, y^{2} + x y = 30$

Created: 3 months ago | Updated: 2 months ago

Job Solution Sonali Bank Ltd Sonali Bank Ltd. || Senior Officer (29-06-2018) || 2018 গণিত

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Solve the following mathematical problems:

Someone plans to invest x taka in the bond of 'M' company, which pays 10% interest and y taka in 'N' company bonds, which pay 9% interest. He will invest 9,000 taka require that he receives 850 taka as interest. How much should be invest in each company?

Created: 3 months ago | Updated: 2 months ago

Job Solution Sonali Bank Ltd Sonali Bank Ltd. || Senior Officer (29-06-2018) || 2018 গণিত

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Solve the following mathematical problems:

A committee of 5 persons is to be formed form 6 male and 5 female members. In how many this committee can be formed so that there is at least 1 male and 1 female member in the committee?

Created: 3 months ago | Updated: 2 months ago

Job Solution Sonali Bank Ltd Sonali Bank Ltd. || Senior Officer (29-06-2018) || 2018 গণিত

Add Description

Solve the following mathematical problems:

A circle is inscribed inside a right angled triangle with equal sides. What is the area of the circle if the length of one side of the right angled triangle is 4cm?

Related Questions

Solve the following mathematical problems:

A teacher has 3 hours to grade all the papers submitted by the 35 students in her class. She gets through the first 5 papers in 30 minutes. How much faster does she have to work to grade the remaining papers in the allotted time?

Solve the following mathematical problems:

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Someone plans to invest x taka in the bond of 'M' company, which pays 10% interest and y taka in 'N' company bonds, which pay 9% interest. He will invest 9,000 taka require that he receives 850 taka as interest. How much should be invest in each company?

Solve the following mathematical problems:

A committee of 5 persons is to be formed form 6 male and 5 female members. In how many this committee can be formed so that there is at least 1 male and 1 female member in the committee?

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