Question

If twice the area of a smaller square is subtracted from the area of a larger square, the result is 14cm². However, if twice the area of the larger square is added to three times the area of the smaller square, the result is 203cm². Determine 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