Guru

# 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

• 0

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,

Share

1. 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

• 0