If twice the area of a smaller square is subtracted from the area of alarger square, the result is 14 cm ². However, if twice the areaof the larger square is added to three times the area of the smallersquare, the result is 203 cm ². Determine the sides of the twosquares.

Let the area of the smaller square be x ² cm ² .
Condition 1: If twice the area of a smaller square is subtracted from the area of a larger square, the result is 14 cm ² .
Then the area of the larger square = (14 + 2x ² ) cm ²
Condition 2: If twice the area of the larger square is added to three times the area of the smaller square, the result is 203 cm ² .
⇒ 2(14 + 2x ² ) + 3 x ² = 203
28 + 4x ² + 3 x ² = 203
7x ² = 175
x ² = 25
x = ± 5 cm
Therefore the sides of smaller square is 5 cm.
And the sides of the larger squares is 14 + 2× 5 ² = 14 + 50 = 64 cm.
The sides of the two squares is 5 cm and 64 cm.
Checking:
a) 64 - 2(5 ² ) = 64 – 250 = 14
b) 2(64) + 3(5 ² ) = 128 + 75 = 203.