Question

if twice the area of a smaller square is subtracted from the area of a larger square is equal to 14 cm however if twice the area of the larger square is added to 3 times the area of the smaller square the result is 203 cm 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

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