Question

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.

Answer 1

Let the side of smaller square = x cm
and side of bigger square = y cm
According to the condition,
y² – 2x² = 14               ...(i)
and 2y² + 3x² = 203   ...(ii)
Multiply (i) by 2 and (ii) by 1
2y² – 4x² = 28
2y² + 3x² = 203
–        –        –  
Subtracting, we get, –7x² = -175

⇒ x² = `(-175)/(-7)` = 25

x² – 25 = 0
⇒ (x + 5)(x - 5) = 0
Either x + 5 = 0,
then x = –5,
but it is not possible
or
x – 5 = 0,
then x = 5.
Substitute the value of x in (i)
y² – 2(5)² = 14
⇒ y² = 14 + 2 x 25
y² = 14 + 50
= 64
= (8)²
∴ y = 8
Hence side of the smaller square = 5 cm
and side of bigger square = 8 cm.