Question

The length of a rectangle exceeds it's width by 5m. If the width is increased by 1m and the length is decreased by 2m the area of the new rectangle is 4sq.m less than the area of the original rectangle. Find the dimensions of the original rectangle

Answer 1

Let the breadth be x
The length be x +5
New breadth = x+1
Area = (x+5)(x+1)=x(x+1)+5(x+1)
=x^2+6x+5
New length =x+5-2=x+3
Area=(x+1)*(x+3)
=x(x+3)+1(x+3)
X^2+4x+3
X^2+4x+3+4=x^2+6x+5
X sq will be canceled from both the sides
4x-6x=5-7
-2x=-2
X=-2/-2=1
Length =6m
Breadth =1m

Answer 2

Let be breadth be x m so length be x+5 m
Area of rectangle by this dimensions =
$x \times (x + 5) = {x}^{2} + 5x \: .....(1)$
Now, when width is increase width be= x+ 5
When length is decrease length be= x+5-2=x+3
$area \: of \: new \: rectangle \: = (x + 5)(x + 3) = {x}^{2} + 3x + 5x + 15 = {x}^{2} + 8x + 15.....(2)$


Therefore, acc/ques
${x}^{2} + 5x \: \: - ({x}^{2} + 8x + 15) = 4 \\ {x}^{2} + 5x - {x}^{2} - 8x - 15 = 4 \\ - 3x - 15 = 4 \\ - 3x = 4 + 15 = 19$
So x = 19/-3 hope it helps u