Question

if twice the area of a smaller square is subtracted from the area of the larger square the result was i4 cm 2 .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.find the sides of the two squares

Answer 1

let the side of the smaller square = a cm

side of the larger square = b cm

twice the area of a smaller square is subtracted from the area of the larger
square =14 cm²
b² - 2a² =14-----(1)
twice the area of the larger square is add to three times the area of the smaller square =203 cm²

2b² + 3a²=203---(2)

multiply (1) with 2 and subtract it from (2)
2b²+3a²=203
2b²-4a²= 14
____________
7a²=175

a²= 175/7
a²=25
a = 5 cm

substitute a =5 in (1)
b²-2a²=14
b²-2*5²=14
b²-50=14
b²=14+50
b²=64
b=8 cm
larger square side = b =8cm
smaller square side = a = 5 cm

Answer 2

Let the area of small square be x.

Then Larger square area = y or 14 + 2x

(Because y - 2x = 14)

          ↓

⇒ 2y + 3x = 203

⇒ 2(14 + 2x) + 3x = 203

⇒ 28 + 4x + 3x = 203

⇒ 7x = 175

⇒ x = 25

_______________________

⇒ y = 14 + 2(25)

⇒ y = 64

Then sides of square is √25 = 5 cm and √64 = 8 cm.