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प्रश्न
Two squares have sides A cm and (x + 4) cm. The sum of their areas is 656 sq. cm.Express this as an algebraic equation and solve it to find the sides of the squares.
उत्तर
Side of first square = x cm .
and side of second square = (x + 4) cm
Now according to the condition,
(x)2 + (x + 4)2 = 656
⇒ x2 – x2 + 8x + 16 = 656
⇒ 2x2 + 8x + 16 – 656 = 0
⇒ 2x2 + 8x – 640 = 0
⇒ x2 + 4x – 320 = 0 ...(Dividing by 2)
⇒ x2 + 20x – 16x – 320 = 0
⇒ x(x + 20) – 16(x + 20) = 0
⇒ (x + 20)(x – 16) = 0
EIther x + 20 = 0,
then x = –20,
but it not possible as it is in negative.
or
x – 16 = 0 then x = 16
Side of first square = 16 cm
and side of second square = 16 + 4 – 4 = 20 cm.
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