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प्रश्न
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.
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उत्तर
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.
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