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 b
b2 – 2a2 = 14 —– (i)
2b2 + 3a2 = 203 —– (ii)
from (i) we have,
b2 = 14 + 2a2
Putting the value of b2 in (ii) we get,
2 (14 + 2a2) + 3a2 = 203
=> 28 + 4a2 + 3a2 = 203
=> 7a2 = 175
=> a2 = 25
=> a = 5 (on neglecting the -ve value)
=> b2 = 14 + 2 (25) = 14 + 50 = 64
=> b = 8 (on neglecting the -ve value)
Hence, a = 4cm and b = 8cm