The length of one pair of opposite sides of a square is increased by 4 cm on each side; the ratio of the length and the breadth of the newly formed rectangle becomes 5 : 3. Find the area of the original square?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 36 cm2
Let the side of the square be \(a\) cm. Lengthening one pair of opposite sides by 4 cm gives a rectangle of length \(a+4\) and breadth \(a\) (the other pair of sides is unchanged), and the ratio of these is 5 : 3.
Length to breadth: \(\displaystyle\frac{a+4}{a}=\frac{5}{3}\)
This gives \(3a+12=5a\), so the side is \(a=6\) cm
Area of the original square \(=6^{2}=\) 36 cm2