This question has been taken from Book:- ML aggarwal, Avichal publication, class10th, quadratic equation in one variable, chapter 5, exercise 5.5

This is an important ques

If twice the area of a smaller square is subtracted from the area of a larger square, the result is 14 cm².

However, if twice the area of the larger square is added to three times the area of the smaller square,

the result is 203 cm². Determine the sides of the two squares

Question no46. , ML Aggarwal, chapter 5, exercise 5.5, quadratic equation in one variable, ICSE board,

Let the length of side of first square (smaller one) be a and that of the other(larger square) be bb^{2}– 2a^{2}= 14 —– (i)2b^{2}+ 3a^{2}= 203 —– (ii)from (i) we have,b^{2}= 14 + 2a^{2}Putting the value of b^{2}in (ii) we get,2 (14 + 2a^{2}) + 3a^{2}= 203=> 28 + 4a^{2}+ 3a^{2}= 203=> 7a^{2}= 175=> a^{2}= 25=> a = 5 (on neglecting the -ve value)=> b^{2}= 14 + 2 (25) = 14 + 50 = 64=> b = 8 (

on neglecting the -ve value)Hence, a = 4cm and b = 8cm