Question

if the length is 2cm more than the breadth and if length and breadth are increased by 2cm each the area gets doubled. find the length and breadth

Answer 1

Case I :
Let the breadth be x and the length be x + 2.
Area = x (x + 2)
= x^2 + 2x
Case II :
Length = x + 2, Breadth = x + 2 + 2 = x + 4
Area = (x + 2)(x + 4)
= x(x + 4) + 2(x + 4)
= x^2 + 4x + 2x + 8
= x^2 + 6x + 8
ATQ,
2(x^2 + 2x) = x^2 + 6x + 8
2x^2 + 4x = x^2 + 6x + 8
2x^2 + 4x - x^2 - 6x = 8
x^2 - 2x = 8
$x = \sqrt{8 + 2x}$