If the side of a square is increased by 8 cm, its area increases by 120 sq. cm. Find the side of the square.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 3.5 cm
Let the side be \(a\) cm. The increase in area is the new area minus the old area, and the new side is \(a+8\).
Increase in area, new square minus old square, which is the given 120 sq. cm: \((a+8)^{2}-a^{2}=120\)
The \(a^{2}\) terms cancel, leaving \(16a+64=120\)
So \(16a=56\) and the side is \(a=3.5\) cm