Question

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.

Answer 1

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.