Question

the length of a rectangular room exceeds its breadth by 4m . if the length is increased by 6m and breadth is diminished by 4m , there would be no change in the area . Find the length and breadth of the room.

Answer 1

Let the breadth be x. Then, the length will be (x+4).
Area of the Rectangle = Length × Breadth = x(x+4) = x² + 4x.

When doing changes, dimensions are as follows:
Length: (x+4)+6 = (x+10)
Breadth: (x-4)
New area = (x-4)(x+10)
= x(x+10)-4(x+10)
= (x²+10x)+(-4x-40)
= x²+(10x-4x)-40
= x²+6x-40

Given: There's no change in areas.

Therefore, x²+4x = x²+6x-40
=> 4x = 6x-40 [Removing x² from both the sides]
=> 6x-4x = 40 => 2x = 40
=> x = 20
Breadth = 20 metres
Length = 24 metres
Also, area = (20×24)m² = 480 m².

Answer 2

hey mate,
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$let \: breadth \: be \: x \\ then \: the \: length \: will \: be \: (x + 4) \\ area \: of \: rectange = l \times b \\ l = (x + 4) = {x}^{2} + 4x \\ b = (x - 4) \\ (x - 4)(x + 10) \\ x(x + 10) - 4(x + 40) \\ ( {x}^{2} + 10x)( - 4x - 40) \\ {x}^{2} + (10x - 4x) - 40 \\ {x}^{2} + 6x - 40 \\ therefore \: {x}^{2} + 4x = {x}^{2} + 6x - 40 \\ 4x = 6x - 40 \\ 6x - 4x = 40 - 2x = 40 \\ x = \frac{40}{2} \\ breadth = 20m \\ length = 24m \\ area = l \times b \\ = (20 \times 24) {m}^{2} \\ = 480 {m}^{2}$
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I hope this helps you
#vaibhav