Geometry

Quadrilaterals

Medium

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?

32 cm²

36 cm²

60 cm²

144 cm²

✅ Correct Option: 2

Let the square's side be $a$ . Lengthening one pair of opposite sides by 4 cm gives a rectangle of dimensions $(a+4)$ by $a$ .

Then $\frac{a+4}{a}=\frac{5}{3}$ , so $3a+12=5a$ and $a=6$ . Area of the square $=6^2=36$ cm².

Note: The phrase 'increased by 4 cm on each side' can also be read as a total gain of 8 cm; we have taken each of the two opposite sides as becoming 4 cm longer.

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Solution

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