Question

the length of the room exceeds its breadth by 3 metres if length is increased by 3 metres and breadth is decreased by 2 metres the area of room remains the same find the length and breadth of the room​

Answer 1

Answer ↦

• Length = 15 m
• Breadth = 12 m

• Given

• Length of the room exceeds its breadth by 3 m.
• If the length is increased by 3 m and breadth is decreased by 2 m.

• To find

• Length and breadth of the room.

• Solution

Let the breadth be x m and length be (x + 3) m.

Area = Length × breadth

⇒ x(x + 3)

⇒ x² + 3x

• Area = x² + 3x

If length is increased by 3 m and breadth is decreased by 2 m. Then,

• New Length = x + 3 + 3 = (x + 6) m
• New breadth = (x - 2) m

⇒ x² + 3x = (x + 6) (x - 2)

⇒ x² + 3x = x(x - 2) + 6(x - 2)

⇒ x² + 3x = x² - 2x + 6x - 12

⇒ 3x - 6x + 2x = - 12

⇒ 5x - 6x = - 12

⇒ - x = - 12

⇒ x = 12

The value of x = 12.

Length and breadth of the room -

• Length = x + 3 = 12 + 3 = 15 m
• Breadth = x = 12 m

Answer 2

Answer:

Length = 15m

Breadth = 12m

Step-by-step explanation:

Let breadth be 'x' m, then the length will be

(x + 3)m

Now,

Area = Length × Breadth

Area = (x + 3)x

Using Distributive Property,

Area = (x² + 3x) m²

But, according to the Question,

(Length + 3m) × (Breadth - 2m) = x² + 3x

Substituting the values,

[(x + 3) + 3] × (x - 2) = x² + 3x

(x + 3 + 3)(x - 2) = x² + 3x

(x + 6)(x - 2) = x² + 3x

Using Distributive Property,

(x × x) + (x × (-2)) + (6 × x) + (6 × (-2)) = x² + 3x

x² - 2x + 6x - 12 = x² + 3x

x² + 4x - 12 = x² + 3x

x² + 4x - 12 - x² = 3x

4x - 12 = 3x

4x - 3x = 12

x = 12 m

Hence,

Breadth = 12m

Then,

Length = x + 3

= 12 + 3 = 15m

Therefore,

Length = 15m

Breadth = 12m

Hope it helped and believing you understood it........All the best