The breadth and length of a rectangle are in the ratio 2:3. In a rectangle with breadth 1 centimetre less than this and length 3 centimetres less, the breadth to length ratio is 3:4. Find the lengths and breadths of both rectangles.

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Solution

Let the breadth of the first rectangle be 2x cm.

Length of the first rectangle = 3x cm

Breadth of the second rectangle = (2x − 1) cm

New length of the second rectangle = (3x − 3) cm

Algebraic form of the problem is:

Subtracting 9x from both the sides:

Adding 4 to both the sides:

∴ Breadth of the first rectangle = 2 × 5 cm = 10 cm

Length of the first rectangle = 3 × 5 = 15 cm

Breadth of the second rectangle = (2 × 5 − 1) cm = 9 cm

Length of the second rectangle = (3 × 5 − 3) cm = 12 cm

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