Question

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

Answer 1

B=x
L=x+3

Area= lb= x(x+3)=x^2+3x

New l= x+3-2=x+1
B=x+3

Ar.= lb= (x+2) (x-1)= x^2-x+2x-2
A/q= x^2-x+2x-2=x^2+3
X-2=3
X=5=b

L=x+3=8

Answer 2

✬ 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)

$\small\implies{\sf }$ (x + 3) (y – 2) = xy

$\small\implies{\sf }$ x (y – 2) + 3 (y – 2) = xy

$\small\implies{\sf }$ xy – 2x + 3y – 6 = xy

$\small\implies{\sf }$ 3y – 2x = 6.........(2)

• Multiply equation by 2 •

$\small\implies{\sf }$ 2 (x – y) = 2 (3)

$\small\implies{\sf }$ 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