Question

The length of a room exceeds its breadth by 3 metres. If the length is increased by 3 metres and the breadth is decreased by 2 metres, the area remains the same. Find the length and the breadth of the room.

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

✬ Length = 15 m ✬

✬ Breadth = 12 m ✬

Step-by-step explanation:

Given:

The length of a room exceeds it's breadth by 3 m

Length is increased by 3 m and breadth is decreased by 2 m then areas remains same.

To Find:

What is length and breadth of the room?

Solution: Let the length of rectangle be x metres and breadth be y metres.

★ Area = Length x Breadth = xy

A/q

Length = x = (y + 3)

x – y = 3 ...............(1)

• Now length is increased by 3 and breadth is decreased by 2 •

New Length = (x + 3)

New Breadth = (y – 2)

⟹ (x + 3) (y – 2) = xy

⟹ x (y – 2) + 3 (y – 2) = xy

⟹ xy – 2x + 3y – 6 = xy

⟹ 3y – 2x = 6.........(2)

• Multiply equation by 2 •

⟹ 2 (x – y) = 2 (3)

⟹ 2x – 2y = 6.........(3)

• Add equation 2 and 3 •

→ 3y – 2x + 2x – 2y = 6 + 6

→ y = 12

Hence, The Breadth of rectangle is y = 12 Metres and Length of rectangle = x = (y + 3)

→ x = 12 + 3 = 15 Metres