A small square region inside a larger squ… | Answer

Subject

Bank Exam

Topic

City Bank Ltd. - Probationary Officer - 2016

A small square region inside a larger square is shaded. The diagonal of the larger square is three times the diagonal of the small square in length. What fraction of the area of the larger square is not shaded ?
Reading

ক)

\(\frac{1}{9}\)

খ)

\(\frac{1}{3}\)

গ)

\(\frac{2}{3}\)

ঘ)

\(\frac{8}{9}\)

Explanation

Solution: অনুবাদঃ একটি বড় বর্গের ভেতরে একটি ছোট বর্গ Shaded (ছায়া করা হয়েছে এমন) করা আছে । বড় বর্গটির কর্ণের দৈর্ঘ্য ছোট বর্গটির কর্ণের দৈর্ঘ্যের তিনগুণ । বড় বর্গের কত অংশ জায়গা Shaded করা হয়নি । ধরি, ছোট বর্গটির কর্ণের দৈর্ঘ্য,

\sqrt 2

a 1 = x .......... (i) বড় বর্গটির কর্ণের দৈর্ঘ্য

\sqrt 2

a 2 = 3x ..............(ii) [ বর্গের এক বাহু a হলে কর্ণের দৈর্ঘ্য

\sqrt 2

a] এখন (i) নং কে (ii) নং দিয়ে ভাগ করে

\frac{{{a_1}}}{{{a_2}}} = \frac{1}{3}

a =

\frac{{{a_2}}}{3}

Unshaded area = বড় বর্গটির ক্ষেত্রফল - ছোট বর্গটির ক্ষেত্রফল = (a 2 ) 2 - (a 1 ) 2 = a 2 2 -

{(\frac{{{a_2}}}{3})^2}

= a 2 2 -

\frac{{{a_{{2^2}}}}}{9}

\frac{{8{a_{{2^2}}}}}{9}

\frac{8}{9}

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A small square region inside a larger square is shaded. The diagonal of the larger square is three times the diagonal of the small square in length. What fraction of the area of the larger square is not shaded ?Reading

A small square region inside a larger square is shaded. The diagonal of the larger square is three times the diagonal of the small square in length. What fraction of the area of the larger square is not shaded ?

Explanation

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A small square region inside a larger square is shaded. The diagonal of the larger square is three times the diagonal of the small square in length. What fraction of the area of the larger square is not shaded ?
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